Complex Langevin and other approaches to the sign problem in quantum many-body physics

Berger, C. E.; Rammelmüller, L.; Loheac, A. C.; Ehmann, F.; Braun, J.; Drut, J. E.

doi:10.1016/j.physrep.2020.09.002

Title: Complex Langevin and other approaches to the sign problem in quantum many-body physics

Journal Article · Wed Oct 07 00:00:00 EDT 2020 · Physics Reports

DOI:https://doi.org/10.1016/j.physrep.2020.09.002· OSTI ID:1850142

Berger, C. E. ^[1]; Rammelmüller, L. ^[2]; Loheac, A. C. ^[1]; Ehmann, F. ^[3]; Braun, J. ^[4]; Drut, J. E. ^[1]

Univ. of North Carolina, Chapel Hill, NC (United States). Dept. of Physics and Astronomy
Technische Univ. Darmstadt (Germany). Institut für Kernphysik (Theoriezentrum); GSI-Helmholtzzentrum fur Schwerionenforschung, Darmstadt (Germany)
Technische Univ. Darmstadt (Germany). Institut für Kernphysik (Theoriezentrum)
Technische Univ. Darmstadt (Germany). Institut für Kernphysik (Theoriezentrum); GSI-Darmstadt (Germany). ExtreMe Matter Inst. (EMMI); FAIR, Facility for Antiproton and Ion Research in Europe GmbH, Darmstadt (Germany)

In this work, we review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard–Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Krell Institute, Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF); German Research Foundation (DFG)

Grant/Contract Number:: FG02-97ER25308; PHY-1452635; 4005/4-1

OSTI ID:: 1850142

Alternate ID(s):: OSTI ID: 1756489

Journal Information:: Physics Reports, Vol. 892, Issue C; ISSN 0370-1573

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (307)

Finite-Temperature Equation of State of Polarized Fermions at Unitarity Rammelmüller, Lukas; Loheac, Andrew C.; Drut, Joaquín E. Physical Review Letters, Vol. 121, Issue 17 https://doi.org/10.1103/PhysRevLett.121.173001	journal	October 2018
Few-body physics on a spacetime lattice in the worldline approach Singh, Hersh; Chandrasekharan, Shailesh Physical Review D, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevD.99.074511	journal	April 2019
Path optimization method for the sign problem Ohnishi, Akira; Mori, Yuto; Kashiwa, Kouji EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507043	journal	January 2018
Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: A comparison with multiparameter reweighting Fodor, Z.; Katz, S. D.; Sexty, D. Physical Review D, Vol. 92, Issue 9 https://doi.org/10.1103/PhysRevD.92.094516	journal	November 2015
QCD at nonzero chemical potential: Recent progress on the lattice Aarts, Gert; Attanasio, Felipe; Jäger, Benjamin XITH CONFERENCE ON QUARK CONFINEMENT AND HADRON SPECTRUM, AIP Conference Proceedings https://doi.org/10.1063/1.4938590	conference	January 2016
Complex Langevin: etiology and diagnostics of its main problem Aarts, Gert; James, Frank A.; Seiler, Erhard The European Physical Journal C, Vol. 71, Issue 10 https://doi.org/10.1140/epjc/s10052-011-1756-5	journal	October 2011
θ dependence of SU(N) gauge theories in the presence of a topological term Vicari, Ettore; Panagopoulos, Haralambos Physics Reports, Vol. 470, Issue 3-4 https://doi.org/10.1016/j.physrep.2008.10.001	journal	January 2009
Spurious solutions of the complex Langevin equation Salcedo, L. L. Physics Letters B, Vol. 305, Issue 1-2 https://doi.org/10.1016/0370-2693(93)91116-5	journal	May 1993
Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin Loheac, Andrew C.; Braun, Jens; Drut, Joaquín E. EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817503007	journal	January 2018
Equation of state for two flavor QCD at nonzero chemical potential Allton, C. R.; Ejiri, S.; Hands, S. J. Physical Review D, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevD.68.014507	journal	July 2003
Particle Projection Using a Complex Langevin Method Shill, Christopher R.; Drut, Joaquín E. EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817503003	journal	January 2018
Toward solving the sign problem with path optimization method Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira Physical Review D, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevD.96.111501	journal	December 2017
Monte Carlo simulations of one-dimensional fermion systems Hirsch, J. E.; Sugar, R. L.; Scalapino, D. J. Physical Review B, Vol. 26, Issue 9 https://doi.org/10.1103/PhysRevB.26.5033	journal	November 1982
Localised distributions and criteria for correctness in complex Langevin dynamics Aarts, Gert; Giudice, Pietro; Seiler, Erhard Annals of Physics, Vol. 337 https://doi.org/10.1016/j.aop.2013.06.019	journal	October 2013
Anomalous decouplings and the fermion sign problem Batrouni, Ghassan George; Scalettar, Richard T. Physical Review B, Vol. 42, Issue 4 https://doi.org/10.1103/PhysRevB.42.2282	journal	August 1990
Lattice Theory for Low Energy Fermions at Nonzero Chemical Potential Chen, Jiunn-Wei; Kaplan, David B. Physical Review Letters, Vol. 92, Issue 25 https://doi.org/10.1103/PhysRevLett.92.257002	journal	June 2004
Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model Ambegaokar, Vinay; Troyer, Matthias American Journal of Physics, Vol. 78, Issue 2 https://doi.org/10.1119/1.3247985	journal	February 2010
Polarized fermions in one dimension: Density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion Loheac, Andrew C.; Braun, Jens; Drut, Joaquín E. Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevD.98.054507	journal	September 2018
Dynamical stabilisation of complex Langevin simulations of QCD Attanasio, Felipe; Jäger, Benjamin The European Physical Journal C, Vol. 79, Issue 1 https://doi.org/10.1140/epjc/s10052-018-6512-7	journal	January 2019
Introductory lectures on lattice QCD at nonzero baryon number Aarts, Gert Journal of Physics: Conference Series, Vol. 706 https://doi.org/10.1088/1742-6596/706/2/022004	journal	April 2016
Spin polarized nonrelativistic fermions in $1 + 1$ dimensions Alexandru, Andrei; Bedaque, Paulo F.; Warrington, Neill C. Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevD.98.054514	journal	September 2018
Density of states approach to dense quantum systems Langfeld, Kurt; Lucini, Biagio Physical Review D, Vol. 90, Issue 9 https://doi.org/10.1103/PhysRevD.90.094502	journal	November 2014
Ultra-cold polarized Fermi gases Chevy, Frédéric; Mora, Christophe Reports on Progress in Physics, Vol. 73, Issue 11 https://doi.org/10.1088/0034-4885/73/11/112401	journal	October 2010
Dual simulation of the 2d U(1) gauge Higgs model at topological angle θ = π: Critical endpoint behavior Gattringer, Christof; Göschl, Daniel; Sulejmanpašić, Tin Nuclear Physics B, Vol. 935 https://doi.org/10.1016/j.nuclphysb.2018.08.017	journal	October 2018
Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin Mollgaard, A.; Splittorff, K. Physical Review D, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevD.91.036007	journal	February 2015
Complex Langevin Simulations of QCD at Finite Density – Progress Report Sinclair, D. K.; Kogut, J. B. EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507031	journal	January 2018
Metropolis Monte Carlo integration on the Lefschetz thimble: Application to a one-plaquette model Mukherjee, Abhishek; Cristoforetti, Marco; Scorzato, Luigi Physical Review D, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevD.88.051502	journal	September 2013
Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem Cristoforetti, Marco; Di Renzo, Francesco; Mukherjee, Abhishek Physical Review D, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevD.88.051501	journal	September 2013
Spectrum of certain non-self-adjoint operators and solutions of Langevin equations with complex drift Klauder, John R.; Petersen, Wesley P. Journal of Statistical Physics, Vol. 39, Issue 1-2 https://doi.org/10.1007/BF01007974	journal	April 1985
Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact Hoffman, M. D.; Javernick, P. D.; Loheac, A. C. Physical Review A, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevA.91.033618	journal	March 2015
Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States Wang, Fugao; Landau, D. P. Physical Review Letters, Vol. 86, Issue 10 https://doi.org/10.1103/PhysRevLett.86.2050	journal	March 2001
Improved convergence of Complex Langevin simulations Attanasio, Felipe; Jäger, Benjamin EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507039	journal	January 2018
Dirac spectrum in complex Langevin simulations of QCD Splittorff, K. Physical Review D, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevD.91.034507	journal	February 2015
Normal State of a Polarized Fermi Gas at Unitarity Lobo, C.; Recati, A.; Giorgini, S. Physical Review Letters, Vol. 97, Issue 20 https://doi.org/10.1103/PhysRevLett.97.200403	journal	November 2006
Complex Langevin solution of the Schwinger model Gausterer, H.; Klauder, J. R. Physical Review Letters, Vol. 56, Issue 4 https://doi.org/10.1103/PhysRevLett.56.306	journal	January 1986
The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions Navon, N.; Nascimbene, S.; Chevy, F. Science, Vol. 328, Issue 5979 https://doi.org/10.1126/science.1187582	journal	April 2010
Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models Sato, Toshihiro; Assaad, Fakher F.; Grover, Tarun Physical Review Letters, Vol. 120, Issue 10 https://doi.org/10.1103/PhysRevLett.120.107201	journal	March 2018
Imaginary chemical potential and finite fermion density on the lattice Alford, Mark; Kapustin, Anton; Wilczek, Frank Physical Review D, Vol. 59, Issue 5 https://doi.org/10.1103/PhysRevD.59.054502	journal	January 1999
Path optimization in $0+1$D QCD at finite density Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira Progress of Theoretical and Experimental Physics, Vol. 2019, Issue 11 https://doi.org/10.1093/ptep/ptz111	journal	November 2019
Langevin simulation in Minkowski space? Gozzi, E. Physics Letters B, Vol. 150, Issue 1-3 https://doi.org/10.1016/0370-2693(85)90152-2	journal	January 1985
The QCD phase diagram for three degenerate flavors and small baryon density de Forcrand, Philippe; Philipsen, Owe Nuclear Physics B, Vol. 673, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2003.09.005	journal	November 2003
Discrete Hubbard-Stratonovich transformation for fermion lattice models Hirsch, J. E. Physical Review B, Vol. 28, Issue 7 https://doi.org/10.1103/PhysRevB.28.4059	journal	October 1983
The complex langevin equation and Monte Carlo simulations of actions with static charges Ambjørn, J.; Flensburg, M.; Peterson, C. Nuclear Physics B, Vol. 275, Issue 3 https://doi.org/10.1016/0550-3213(86)90605-X	journal	November 1986
Complex Langevin method applied to the 2D $S U (2)$ Yang-Mills theory Makino, Hiroki; Suzuki, Hiroshi; Takeda, Daisuke Physical Review D, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevD.92.085020	journal	October 2015
Chiral effective field theory and nuclear forces Machleidt, R.; Entem, D. R. Physics Reports, Vol. 503, Issue 1 https://doi.org/10.1016/j.physrep.2011.02.001	journal	June 2011
Lattice study of the Silver Blaze phenomenon for a charged scalar field Gattringer, Christof; Kloiber, Thomas Nuclear Physics B, Vol. 869, Issue 1 https://doi.org/10.1016/j.nuclphysb.2012.12.005	journal	April 2013
Stochastic quantization of thermal fermions on the real-time Keldysh contour Kolley, E.; Kolley, W. Physics Letters A, Vol. 129, Issue 4 https://doi.org/10.1016/0375-9601(88)90351-9	journal	May 1988
Imbalanced Feshbach-resonant Fermi gases Radzihovsky, Leo; Sheehy, Daniel E. Reports on Progress in Physics, Vol. 73, Issue 7 https://doi.org/10.1088/0034-4885/73/7/076501	journal	June 2010
The QCD deconfinement transition for heavy quarks and all baryon chemical potentials Fromm, Michael; Langelage, Jens; Lottini, Stefano Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)042	journal	January 2012
Sufficient condition for absence of the sign problem in the fermionic quantum Monte Carlo algorithm Wu, Congjun; Zhang, Shou-Cheng Physical Review B, Vol. 71, Issue 15 https://doi.org/10.1103/PhysRevB.71.155115	journal	April 2005
Lattice theory for nonrelativistic fermions in one spatial dimension Endres, Michael G. Physical Review A, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevA.85.063624	journal	June 2012
Critical line of two-flavor QCD at finite isospin or baryon densities from imaginary chemical potentials Cea, Paolo; Cosmai, Leonardo; D’Elia, Massimo Physical Review D, Vol. 85, Issue 9 https://doi.org/10.1103/PhysRevD.85.094512	journal	May 2012
Auxiliary-field quantum Monte Carlo method for strongly paired fermions Carlson, J.; Gandolfi, Stefano; Schmidt, Kevin E. Physical Review A, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRevA.84.061602	journal	December 2011
Modern theory of nuclear forces Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G. Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/RevModPhys.81.1773	journal	December 2009
Strongly interacting quark-gluon plasma, and the critical behavior of QCD at imaginary $μ$ D’Elia, Massimo; Di Renzo, Francesco; Lombardo, Maria Paola Physical Review D, Vol. 76, Issue 11 https://doi.org/10.1103/PhysRevD.76.114509	journal	December 2007
Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions Rammelmüller, Lukas; Porter, William J.; Drut, Joaquín E. Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.094506	journal	November 2017
Alternating descent method for gauge cooling of complex Langevin simulations Dong, Xiaoyu; Cai, Zhenning; Di, Yana Physical Review D, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevD.102.054518	journal	September 2020
Cooper Pairing Above the Critical Temperature in a Unitary Fermi Gas Wlazłowski, Gabriel; Magierski, Piotr; Drut, Joaquín E. Physical Review Letters, Vol. 110, Issue 9 https://doi.org/10.1103/PhysRevLett.110.090401	journal	February 2013
Complex Langevin Simulation Okano, Keisuke; Schülke, Lothar; Zheng, Bo Progress of Theoretical Physics Supplement, Vol. 111 https://doi.org/10.1143/PTPS.111.313	journal	January 1993
Langevin algorithms for spin models Catterall, S. M.; Drummond, I. T.; Horgan, R. R. Physics Letters B, Vol. 254, Issue 1-2 https://doi.org/10.1016/0370-2693(91)90417-O	journal	January 1991
Zero-Temperature Equation of State of Mass-Imbalanced Resonant Fermi Gases Braun, Jens; Drut, Joaquín E.; Roscher, Dietrich Physical Review Letters, Vol. 114, Issue 5 https://doi.org/10.1103/PhysRevLett.114.050404	journal	February 2015
Complex Langevin dynamics for chiral random matrix theory Mollgaard, A.; Splittorff, K. Physical Review D, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevD.88.116007	journal	December 2013
Binding of holes in the Hubbard model Dagotto, E.; Moreo, A.; Sugar, R. L. Physical Review B, Vol. 41, Issue 1 https://doi.org/10.1103/PhysRevB.41.811	journal	January 1990
Positive representations of complex distributions on groups Salcedo, L. L. Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 50 https://doi.org/10.1088/1751-8121/aaea16	journal	November 2018
Imaginary Polarization as a Way to Surmount the Sign Problem in Ab Initio Calculations of Spin-Imbalanced Fermi Gases Braun, Jens; Chen, Jiunn-Wei; Deng, Jian Physical Review Letters, Vol. 110, Issue 13 https://doi.org/10.1103/PhysRevLett.110.130404	journal	March 2013
Analytic continuation of Chern-Simons theory Witten, Edward Chern-Simons Gauge Theory: 20 Years After https://doi.org/10.1090/amsip/050/19	book	January 2010
Fermi gases in one dimension: From Bethe ansatz to experiments Guan, Xi-Wen; Batchelor, Murray T.; Lee, Chaohong Reviews of Modern Physics, Vol. 85, Issue 4 https://doi.org/10.1103/RevModPhys.85.1633	journal	November 2013
Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong Physical Review Letters, Vol. 117, Issue 26 https://doi.org/10.1103/PhysRevLett.117.267002	journal	December 2016
Representation of complex probabilities Salcedo, L. L. Journal of Mathematical Physics, Vol. 38, Issue 3 https://doi.org/10.1063/1.531906	journal	March 1997
Langevin simulations of a long-range electron-phonon model Batrouni, G. G.; Scalettar, Richard T. Physical Review B, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevB.99.035114	journal	January 2019
Schwinger-Keldysh formalism on the lattice: A faster algorithm and its application to field theory Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F. Physical Review D, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevD.95.114501	journal	June 2017
An Introduction to Effective Field Theory Burgess, C. P. Annual Review of Nuclear and Particle Science, Vol. 57, Issue 1 https://doi.org/10.1146/annurev.nucl.56.080805.140508	journal	November 2007
Phase diagram of a two-component Fermi gas with resonant interactions Shin, Yong-il; Schunck, Christian H.; Schirotzek, André Nature, Vol. 451, Issue 7179 https://doi.org/10.1038/nature06473	journal	February 2008
Lattice gauge theory without link variables Vairinhos, Hélvio; de Forcrand, Philippe Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)038	journal	December 2014
Complex Langevin simulations of non-Abelian integrals Haymaker, Richard W.; Wosiek, J. Physical Review D, Vol. 37, Issue 4 https://doi.org/10.1103/PhysRevD.37.969	journal	February 1988
Application of a neural network to the sign problem via the path optimization method Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 2 https://doi.org/10.1093/ptep/ptx191	journal	February 2018
Transdimensional Equivalence of Universal Constants for Fermi Gases at Unitarity Endres, Michael G. Physical Review Letters, Vol. 109, Issue 25 https://doi.org/10.1103/PhysRevLett.109.250403	journal	December 2012
Complex Langevin: A numerical method? Gausterer, H. Nuclear Physics A, Vol. 642, Issue 1-2 https://doi.org/10.1016/S0375-9474(98)00522-3	journal	November 1998
The pseudogap regime in the unitary Fermi gas Jensen, S.; Gilbreth, C. N.; Alhassid, Y. The European Physical Journal Special Topics, Vol. 227, Issue 15-16 https://doi.org/10.1140/epjst/e2019-800105-y	journal	March 2019
Selected inversion as key to a stable Langevin evolution across the QCD phase boundary Bloch, Jacques; Schenk, Olaf EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507003	journal	January 2018
Can Stochastic Quantization Evade the Sign Problem? The Relativistic Bose Gas at Finite Chemical Potential Aarts, Gert Physical Review Letters, Vol. 102, Issue 13 https://doi.org/10.1103/PhysRevLett.102.131601	journal	April 2009
Spin and charge dynamics of the ferromagnetic and antiferromagnetic two-dimensional half-filled Kondo lattice model Capponi, S.; Assaad, F. F. Physical Review B, Vol. 63, Issue 15 https://doi.org/10.1103/PhysRevB.63.155114	journal	March 2001
Developments in lattice quantum chromodynamics for matter at high temperature and density Aarts, Gert Pramana, Vol. 84, Issue 5 https://doi.org/10.1007/s12043-015-0981-0	journal	May 2015
Monte Carlo Study of Real Time Dynamics on the Lattice Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F. Physical Review Letters, Vol. 117, Issue 8 https://doi.org/10.1103/PhysRevLett.117.081602	journal	August 2016
The second order Langevin equation and numerical simulations Horowitz, Alan M. Nuclear Physics B, Vol. 280 https://doi.org/10.1016/0550-3213(87)90159-3	journal	January 1987
Sign problem and Monte Carlo calculations beyond Lefschetz thimbles Alexandru, Andrei; Basar, Gökçe; Bedaque, Paulo F. Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)053	journal	May 2016
Density of States in Gauge Theories Langfeld, Kurt; Lucini, Biagio; Rago, Antonio Physical Review Letters, Vol. 109, Issue 11 https://doi.org/10.1103/PhysRevLett.109.111601	journal	September 2012
Heavy dense QCD and nuclear matter from an effective lattice theory Langelage, Jens; Neuman, Mathias; Philipsen, Owe Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)131	journal	September 2014
Density of states method for the $Z_{3}$ spin model Gattringer, Christof; Törek, Pascal Physics Letters B, Vol. 747 https://doi.org/10.1016/j.physletb.2015.06.017	journal	July 2015
Crystalline color superconductors Anglani, Roberto; Casalbuoni, Roberto; Ciminale, Marco Reviews of Modern Physics, Vol. 86, Issue 2 https://doi.org/10.1103/RevModPhys.86.509	journal	April 2014
The shell model Monte Carlo approach to level densities: Recent developments and perspectives Alhassid, Y. The European Physical Journal A, Vol. 51, Issue 12 https://doi.org/10.1140/epja/i2015-15171-3	journal	December 2015
Fermi gases with imaginary mass imbalance and the sign problem in Monte-Carlo calculations Roscher, Dietrich; Braun, Jens; Chen, Jiunn-Wei Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 5 https://doi.org/10.1088/0954-3899/41/5/055110	journal	March 2014
Complex Langevin simulations and the QCD phase diagram: recent developments Attanasio, Felipe; Jäger, Benjamin; Ziegler, Felix P. G. The European Physical Journal A, Vol. 56, Issue 10 https://doi.org/10.1140/epja/s10050-020-00256-z	journal	October 2020
Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases Rammelmüller, Lukas; Drut, Joaquín E.; Braun, Jens SciPost Physics, Vol. 9, Issue 1 https://doi.org/10.21468/SciPostPhys.9.1.014	journal	January 2020
Quantum Monte Carlo with directed loops Syljuåsen, Olav F.; Sandvik, Anders W. Physical Review E, Vol. 66, Issue 4 https://doi.org/10.1103/PhysRevE.66.046701	journal	October 2002
Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids Fredrickson, Glenn H.; Ganesan, Venkat; Drolet, François Macromolecules, Vol. 35, Issue 1 https://doi.org/10.1021/ma011515t	journal	January 2002
Controlling complex Langevin simulations of lattice models by boundary term analysis Scherzer, M.; Seiler, E.; Sexty, D. Physical Review D, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevD.101.014501	journal	January 2020
Ab initio study of the thermodynamics of quantum chromodynamics on the lattice at zero and finite densities Ejiri, Shinji; Kanaya, Kazuyuki; Umeda, Takashi Progress of Theoretical and Experimental Physics, Vol. 2012, Issue 1 https://doi.org/10.1093/ptep/pts005	journal	January 2012
An efficient method to compute the residual phase on a Lefschetz thimble Cristoforetti, M.; Di Renzo, F.; Eruzzi, G. Physical Review D, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevD.89.114505	journal	June 2014
Isentropic equation of state of 2-flavor QCD Ejiri, S.; Karsch, F.; Laermann, E. Physical Review D, Vol. 73, Issue 5 https://doi.org/10.1103/PhysRevD.73.054506	journal	March 2006
The QCD Equation of state and critical end-point estimates at $O (μ_{B}^{6})$ Sharma, Sayantan Nuclear Physics A, Vol. 967 https://doi.org/10.1016/j.nuclphysa.2017.05.008	journal	November 2017
Status of Complex Langevin Seiler, Erhard EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817501019	journal	January 2018
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
The density of states method at non-zero chemical potential Fodor, Zoltan; Katz, Sandor D.; Schmidt, Christian Journal of High Energy Physics, Vol. 2007, Issue 03 https://doi.org/10.1088/1126-6708/2007/03/121	journal	March 2007
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/RevModPhys.79.291	journal	February 2007
Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations Wang, Lei; Liu, Ye-Hua; Iazzi, Mauro Physical Review Letters, Vol. 115, Issue 25 https://doi.org/10.1103/PhysRevLett.115.250601	journal	December 2015
Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks Fromm, M.; Langelage, J.; Lottini, S. Physical Review Letters, Vol. 110, Issue 12 https://doi.org/10.1103/PhysRevLett.110.122001	journal	March 2013
Pairing in asymmetric many-fermion systems: Functional renormalisation group approach Krippa, Boris Physics Letters B, Vol. 744 https://doi.org/10.1016/j.physletb.2015.03.057	journal	May 2015
Fermion bag approach to lattice field theories Chandrasekharan, Shailesh Physical Review D, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevD.82.025007	journal	July 2010
Worm algorithms for the 3-state Potts model with magnetic field and chemical potential Mercado, Ydalia Delgado; Evertz, Hans Gerd; Gattringer, Christof Computer Physics Communications, Vol. 183, Issue 9 https://doi.org/10.1016/j.cpc.2012.04.014	journal	September 2012
Field-theoretic polymer simulations Ganesan, V.; Fredrickson, G. H. Europhysics Letters (EPL), Vol. 55, Issue 6 https://doi.org/10.1209/epl/i2001-00353-8	journal	September 2001
How does Gauge Cooling Stabilize Complex Langevin? Cai, Zhenning Communications in Computational Physics, Vol. 27, Issue 5 https://doi.org/10.4208/cicp.OA-2019-0126	journal	February 2020
Tempered transitions between thimbles Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F. Physical Review D, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevD.96.034513	journal	August 2017
Progress in complex Langevin simulations of full QCD at non-zero density Sexty, Dénes Nuclear Physics A, Vol. 931 https://doi.org/10.1016/j.nuclphysa.2014.09.029	journal	November 2014
Real-time gauge theory simulations from stochastic quantization with optimized updating Berges, Jürgen; Sexty, Dénes Nuclear Physics B, Vol. 799, Issue 3 https://doi.org/10.1016/j.nuclphysb.2008.01.018	journal	August 2008
Two complex problems on the lattice: transport coefficients and finite chemical potential Aarts, Gert Nuclear Physics A, Vol. 820, Issue 1-4 https://doi.org/10.1016/j.nuclphysa.2009.01.019	journal	April 2009
The stochastic method for numerical simulations: Drummond, I. T.; Duane, S.; Horgan, R. R. Nuclear Physics B, Vol. 220, Issue 1 https://doi.org/10.1016/0550-3213(83)90137-2	journal	May 1983
The Fokker-Planck equations in lattice gauge theories Xue, She-Sheng Physics Letters B, Vol. 180, Issue 3 https://doi.org/10.1016/0370-2693(86)90309-6	journal	November 1986
Shifted-contour auxiliary-field Monte Carlo: circumventing the sign difficulty for electronic-structure calculations Rom, Naomi; Charutz, D. M.; Neuhauser, Daniel Chemical Physics Letters, Vol. 270, Issue 3-4 https://doi.org/10.1016/S0009-2614(97)00370-9	journal	May 1997
Coherent states formulation of polymer field theory Man, Xingkun; Delaney, Kris T.; Villet, Michael C. The Journal of Chemical Physics, Vol. 140, Issue 2 https://doi.org/10.1063/1.4860978	journal	January 2014
Structure of Lefschetz thimbles in simple fermionic systems Kanazawa, Takuya; Tanizaki, Yuya Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)044	journal	March 2015
Argument for justification of the complex Langevin method and the condition for correct convergence Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji Physical Review D, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevD.94.114515	journal	December 2016
Monte Carlo versus Langevin methods for nonpositive definite weights Lin, H. Q.; Hirsch, J. E. Physical Review B, Vol. 34, Issue 3 https://doi.org/10.1103/PhysRevB.34.1964	journal	August 1986
$M$ theory as a matrix model: A conjecture Banks, T.; Fischler, W.; Shenker, S. H. Physical Review D, Vol. 55, Issue 8 https://doi.org/10.1103/PhysRevD.55.5112	journal	April 1997
Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited Aarts, Gert; James, Frank A. Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)118	journal	January 2012
Lattice simulations of real-time quantum fields Berges, J.; Borsányi, Sz.; Sexty, D. Physical Review D, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevD.75.045007	journal	February 2007
Field-theoretic simulations of polyelectrolyte complexation Popov, Yuri O.; Lee, Jonghoon; Fredrickson, Glenn H. Journal of Polymer Science Part B: Polymer Physics, Vol. 45, Issue 24 https://doi.org/10.1002/polb.21334	journal	January 2007
Monte Carlo calculations of the finite density Thirring model Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F. Physical Review D, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevD.95.014502	journal	January 2017
Simulating full QCD at nonzero density using the complex Langevin equation Sexty, Dénes Physics Letters B, Vol. 729 https://doi.org/10.1016/j.physletb.2014.01.019	journal	February 2014
Thermal equation of state of polarized fermions in one dimension via complex chemical potentials Loheac, Andrew C.; Braun, Jens; Drut, Joaquín E. Physical Review A, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevA.92.063609	journal	December 2015
Applying complex Langevin simulations to lattice QCD at finite density Kogut, J. B.; Sinclair, D. K. Physical Review D, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevD.100.054512	journal	September 2019
Simulating Lattice QCD at Finite Density Gocksch, Andreas Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2054	journal	October 1988
Stochastic quantization at finite chemical potential Aarts, Gert; Stamatescu, Ion-Olimpiu Journal of High Energy Physics, Vol. 2008, Issue 09 https://doi.org/10.1088/1126-6708/2008/09/018	journal	September 2008
Quantum Monte Carlo study of mass-imbalanced Hubbard models Liu, Ye-Hua; Wang, Lei Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235129	journal	December 2015
Hybrid-molecular-dynamics algorithms for the numerical simulation of quantum chromodynamics Gottlieb, Steven; Liu, W.; Toussaint, D. Physical Review D, Vol. 35, Issue 8 https://doi.org/10.1103/PhysRevD.35.2531	journal	April 1987
Complex Langevin method: When can it be trusted? Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu Physical Review D, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevD.81.054508	journal	March 2010
Applying the tempered Lefschetz thimble method to the Hubbard model away from half filling Fukuma, Masafumi; Matsumoto, Nobuyuki; Umeda, Naoya Physical Review D, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevD.100.114510	journal	December 2019
Unification of the complex Langevin method and the Lefschetzthimble method Nishimura, Jun; Shimasaki, Shinji EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507018	journal	January 2018
Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method Ito, Yuta; Nishimura, Jun EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507019	journal	January 2018
Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique Nagata, Keitro; Nishimura, Jun; Shimasaki, Shinji EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817507017	journal	January 2018
Adaptive stepsize and instabilities in complex Langevin dynamics Aarts, Gert; James, Frank A.; Seiler, Erhard Physics Letters B, Vol. 687, Issue 2-3 https://doi.org/10.1016/j.physletb.2010.03.012	journal	April 2010
Fluctuation Effects in Ternary AB + A + B Polymeric Emulsions Düchs, Dominik; Ganesan, Venkat; Fredrickson, Glenn H. Macromolecules, Vol. 36, Issue 24 https://doi.org/10.1021/ma030201y	journal	December 2003
Simulating Nonequilibrium Quantum Fields with Stochastic Quantization Techniques Berges, J.; Stamatescu, I. -O. Physical Review Letters, Vol. 95, Issue 20 https://doi.org/10.1103/PhysRevLett.95.202003	journal	November 2005
Hybrid Monte Carlo on Lefschetz thimbles — A study of the residual sign problem Fujii, H.; Honda, D.; Kato, M. Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)147	journal	October 2013
Controlling complex Langevin dynamics at finite density Aarts, Gert; Bongiovanni, Lorenzo; Seiler, Erhard The European Physical Journal A, Vol. 49, Issue 7 https://doi.org/10.1140/epja/i2013-13089-4	journal	July 2013
A multi-species exchange model for fully fluctuating polymer field theory simulations Düchs, Dominik; Delaney, Kris T.; Fredrickson, Glenn H. The Journal of Chemical Physics, Vol. 141, Issue 17 https://doi.org/10.1063/1.4900574	journal	November 2014
Exact analysis of a δ-function spin-1/2 attractive Fermi gas with arbitrary polarization Iida, Toshiaki; Wadati, Miki Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 06 https://doi.org/10.1088/1742-5468/2007/06/P06011	journal	June 2007
Exploring the thermodynamics of a universal Fermi gas Nascimbène, S.; Navon, N.; Jiang, K. J. Nature, Vol. 463, Issue 7284 https://doi.org/10.1038/nature08814	journal	February 2010
Hybrid Monte Carlo Duane, Simon; Kennedy, A. D.; Pendleton, Brian J. Physics Letters B, Vol. 195, Issue 2 https://doi.org/10.1016/0370-2693(87)91197-X	journal	September 1987
Phase structure of mass- and spin-imbalanced unitary Fermi gases Roscher, Dietrich; Braun, Jens; Drut, Joaquín E. Physical Review A, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevA.91.053611	journal	May 2015
Benchmark results in the 2D lattice Thirring model with a chemical potential Ayyar, Venkitesh; Chandrasekharan, Shailesh; Rantaharju, Jarno Physical Review D, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevD.97.054501	journal	March 2018
Ab initio no core shell model Barrett, Bruce R.; Navrátil, Petr; Vary, James P. Progress in Particle and Nuclear Physics, Vol. 69 https://doi.org/10.1016/j.ppnp.2012.10.003	journal	March 2013
Fast estimator of Jacobians in the Monte Carlo integration on Lefschetz thimbles Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F. Physical Review D, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevD.93.094514	journal	May 2016
On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential Aarts, Gert; James, Frank A. Journal of High Energy Physics, Vol. 2010, Issue 8 https://doi.org/10.1007/JHEP08(2010)020	journal	August 2010
Finite density QCD via an imaginary chemical potential D’Elia, Massimo; Lombardo, Maria-Paola Physical Review D, Vol. 67, Issue 1 https://doi.org/10.1103/PhysRevD.67.014505	journal	January 2003
Test for a universal behavior of Dirac eigenvalues in the complex Langevin method Ichihara, Terukazu; Nagata, Keitaro; Kashiwa, Kouji Physical Review D, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevD.93.094511	journal	May 2016
Charge and spin structures of a $d_{x^{2} - y^{2}}$ superconductor in the proximity of an antiferromagnetic Mott insulator Assaad, F. F.; Imada, M.; Scalapino, D. J. Physical Review B, Vol. 56, Issue 23 https://doi.org/10.1103/PhysRevB.56.15001	journal	December 1997
Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model Hayata, Tomoya; Yamamoto, Arata Physical Review B, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevB.96.035129	journal	July 2017
Lefschetz thimbles and stochastic quantization: Complex actions in the complex plane Aarts, Gert Physical Review D, Vol. 88, Issue 9 https://doi.org/10.1103/PhysRevD.88.094501	journal	November 2013
Two-color QCD with heavy quarks at finite densities Langfeld, Kurt; Pawlowski, Jan M. Physical Review D, Vol. 88, Issue 7 https://doi.org/10.1103/PhysRevD.88.071502	journal	October 2013
Fermion bag approach to fermion sign problems: New opportunities in lattice fermion field theories Chandrasekharan, Shailesh The European Physical Journal A, Vol. 49, Issue 7 https://doi.org/10.1140/epja/i2013-13090-y	journal	July 2013
Complex Langevin for semisimple compact connected Lie groups and U (1) Gausterer, H.; Thaler, H. Journal of Physics A: Mathematical and General, Vol. 31, Issue 11 https://doi.org/10.1088/0305-4470/31/11/006	journal	March 1998
Complex Langevin equations and lattice gauge theory Flower, Jon; Otto, Steve W.; Callahan, Sean Physical Review D, Vol. 34, Issue 2 https://doi.org/10.1103/PhysRevD.34.598	journal	July 1986
Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas Ku, M. J. H.; Sommer, A. T.; Cheuk, L. W. Science, Vol. 335, Issue 6068 https://doi.org/10.1126/science.1214987	journal	January 2012
Superfluid condensate fraction and pairing wave function of the unitary Fermi gas He, Rongzheng; Li, Ning; Lu, Bing-Nan Physical Review A, Vol. 101, Issue 6 https://doi.org/10.1103/PhysRevA.101.063615	journal	June 2020
QCD equation of state to $O (μ_{B}^{6})$ from lattice QCD Bazavov, A.; Ding, H. -T.; Hegde, P. Physical Review D, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevD.95.054504	journal	March 2017
Complex Langevin simulations of zero-dimensional supersymmetric quantum field theories Joseph, Anosh; Kumar, Arpith Physical Review D, Vol. 100, Issue 7 https://doi.org/10.1103/PhysRevD.100.074507	journal	October 2019
Comparison of algorithms for solving the sign problem in the O(3) model in $1 + 1$ dimensions at finite chemical potential Katz, S. D.; Niedermayer, F.; Nógrádi, D. Physical Review D, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevD.95.054506	journal	March 2017
Random Matrix Theory and Chiral Symmetry in QCD Verbaarschot, J. J. M.; Wettig, T. Annual Review of Nuclear and Particle Science, Vol. 50, Issue 1 https://doi.org/10.1146/annurev.nucl.50.1.343	journal	December 2000
Fulde-Ferrell-Larkin-Ovchinnikov state in the one-dimensional attractive Hubbard model and its fingerprint in spatial noise correlations Lüscher, Andreas; Noack, Reinhard M.; Läuchli, Andreas M. Physical Review A, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevA.78.013637	journal	July 2008
Simulating the all-order strong coupling expansion I: Ising model demo Wolff, Ulli Nuclear Physics B, Vol. 810, Issue 3 https://doi.org/10.1016/j.nuclphysb.2008.09.033	journal	April 2009
Reweighting complex Langevin trajectories Bloch, Jacques Physical Review D, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevD.95.054509	journal	March 2017
Renormalization Group Theory for the Imbalanced Fermi Gas Gubbels, K. B.; Stoof, H. T. C. Physical Review Letters, Vol. 100, Issue 14 https://doi.org/10.1103/PhysRevLett.100.140407	journal	April 2008
Fermion Bags, Duality, and the Three Dimensional Massless Lattice Thirring Model Chandrasekharan, Shailesh; Li, Anyi Physical Review Letters, Vol. 108, Issue 14 https://doi.org/10.1103/PhysRevLett.108.140404	journal	April 2012
Efficient simulation of relativistic fermions via vertex models Wenger, Urs Physical Review D, Vol. 80, Issue 7 https://doi.org/10.1103/PhysRevD.80.071503	journal	October 2009
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji Physical Review D, Vol. 91, Issue 10 https://doi.org/10.1103/PhysRevD.91.101701	journal	May 2015
Complex Langevin dynamics and zeroes of the fermion determinant Aarts, Gert; Seiler, Erhard; Sexty, Dénes Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)044	journal	May 2017
Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential Aarts, Gert; Splittorff, K. Journal of High Energy Physics, Vol. 2010, Issue 8 https://doi.org/10.1007/JHEP08(2010)017	journal	August 2010
Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong New Journal of Physics, Vol. 17, Issue 8 https://doi.org/10.1088/1367-2630/17/8/085003	journal	August 2015
Numerical study of the unitary Fermi gas across the superfluid transition Goulko, Olga; Wingate, Matthew Physical Review A, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevA.93.053604	journal	May 2016
Exact duality and dual Monte Carlo simulation for the bosonic Hubbard model Hébert, F.; Batrouni, G. G.; Mabilat, H. Physical Review B, Vol. 61, Issue 16 https://doi.org/10.1103/PhysRevB.61.10725	journal	April 2000
On the ground state energy of the delta-function Fermi gas Tracy, Craig A.; Widom, Harold Journal of Mathematical Physics, Vol. 57, Issue 10 https://doi.org/10.1063/1.4964252	journal	October 2016
The existence of positive representations for complex weights Salcedo, L. L. Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue 31 https://doi.org/10.1088/1751-8113/40/31/016	journal	July 2007
Fermion bag approach for the massive Thirring model at finite density Li, Daming Physical Review D, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevD.94.114501	journal	December 2016
New Monte Carlo technique for studying phase transitions Ferrenberg, Alan M.; Swendsen, Robert H. Physical Review Letters, Vol. 61, Issue 23 https://doi.org/10.1103/PhysRevLett.61.2635	journal	December 1988
Finite-density Monte Carlo calculations on sign-optimized manifolds Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry Physical Review D, Vol. 97, Issue 9 https://doi.org/10.1103/PhysRevD.97.094510	journal	May 2018
Does the complex Langevin method give unbiased results? Salcedo, L. L. Physical Review D, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevD.94.114505	journal	December 2016
Fermion bag approach to Hamiltonian lattice field theories in continuous time Huffman, Emilie; Chandrasekharan, Shailesh Physical Review D, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevD.96.114502	journal	December 2017
Complex Langevin solution to an effective theory of lattice QCD Bilić, Neven; Gausterer, H.; Sanielevici, S. Physical Review D, Vol. 37, Issue 12 https://doi.org/10.1103/PhysRevD.37.3684	journal	June 1988
How to get from imaginary to real chemical potential Karbstein, Felix; Thies, Michael Physical Review D, Vol. 75, Issue 2 https://doi.org/10.1103/PhysRevD.75.025003	journal	January 2007
Gibbs sampling of complex-valued distributions Salcedo, L. L. Physical Review D, Vol. 94, Issue 7 https://doi.org/10.1103/PhysRevD.94.074503	journal	October 2016
Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method Fukushima, K.; Tanizaki, Y. Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 11 https://doi.org/10.1093/ptep/ptv152	journal	September 2015
A Langevin approach to fermion and quantum spin correlation functions Klauder, J. R. Journal of Physics A: Mathematical and General, Vol. 16, Issue 10 https://doi.org/10.1088/0305-4470/16/10/001	journal	July 1983
Dual simulation of the two-dimensional lattice U(1) gauge-Higgs model with a topological term Gattringer, Christof; Kloiber, Thomas; Müller-Preussker, Michael Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114508	journal	December 2015
The QCD equation of state at finite density from analytical continuation Guenther, J. N.; Bellwied, R.; Borsányi, S. Nuclear Physics A, Vol. 967 https://doi.org/10.1016/j.nuclphysa.2017.05.044	journal	November 2017
New insights into the problem with a singular drift term in the complex Langevin method Nishimura, Jun; Shimasaki, Shinji Physical Review D, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevD.92.011501	journal	July 2015
Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model Nishimura, Jun; Tsuchiya, Asato Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/JHEP06(2019)077	journal	June 2019
Imaginary noise and parity conservation in the reaction A+A⇌0 Deloubrière, O.; Frachebourg, L.; Hilhorst, H. J. Physica A: Statistical Mechanics and its Applications, Vol. 308, Issue 1-4 https://doi.org/10.1016/S0378-4371(02)00548-4	journal	May 2002
Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas Gattringer, Christof; Kloiber, Thomas Physics Letters B, Vol. 720, Issue 1-3 https://doi.org/10.1016/j.physletb.2013.01.068	journal	March 2013
A Stochastic Approximation Method Robbins, Herbert; Monro, Sutton The Annals of Mathematical Statistics, Vol. 22, Issue 3 https://doi.org/10.1214/aoms/1177729586	journal	September 1951
Formation of selfbound states in a one-dimensional nuclear model—a renormalization group based density functional study Kemler, Sandra; Pospiech, Martin; Braun, Jens Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 1 https://doi.org/10.1088/0954-3899/44/1/015101	journal	December 2016
Thermodynamics of spin-orbit-coupled bosons in two dimensions from the complex Langevin method Attanasio, Felipe; Drut, Joaquín E. Physical Review A, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevA.101.033617	journal	March 2020
Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications Li, Zi-Xiang; Yao, Hong Annual Review of Condensed Matter Physics, Vol. 10, Issue 1 https://doi.org/10.1146/annurev-conmatphys-033117-054307	journal	March 2019
QCD Phase Diagram According to the Center Group Mercado, Ydalia Delgado; Evertz, Hans Gerd; Gattringer, Christof Physical Review Letters, Vol. 106, Issue 22 https://doi.org/10.1103/PhysRevLett.106.222001	journal	June 2011
Comparison of complex Langevin and mean field methods applied to effective Polyakov line models Greensite, Jeff Physical Review D, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevD.90.114507	journal	December 2014
Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion Aarts, Gert; Seiler, Erhard; Sexty, Dénes Physical Review D, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevD.90.114505	journal	December 2014
The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics Aarts, Gert; Attanasio, Felipe; Jäger, Benjamin Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)087	journal	September 2016
Complex Langevin Simulation of the SU(3) Spin Model with Nonzero Chemical Potential Karsch, F.; Wyld, H. W. Physical Review Letters, Vol. 55, Issue 21 https://doi.org/10.1103/PhysRevLett.55.2242	journal	November 1985
A complex Langevin approach to ultracold fermions Rammelmüller, Lukas; Drut, Joaquín E.; Braun, Jens Journal of Physics: Conference Series, Vol. 1041 https://doi.org/10.1088/1742-6596/1041/1/012006	journal	June 2018
Approaches to the sign problem in lattice field theory Gattringer, Christof; Langfeld, Kurt International Journal of Modern Physics A, Vol. 31, Issue 22 https://doi.org/10.1142/S0217751X16430077	journal	August 2016
Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension Loheac, Andrew C.; Drut, Joaquín E. Physical Review D, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevD.95.094502	journal	May 2017
Advances in non-relativistic matter via complex Langevin approaches Drut, Joaquín E. Journal of Physics: Conference Series, Vol. 1041 https://doi.org/10.1088/1742-6596/1041/1/012005	journal	June 2018
Phase structure of spin-imbalanced unitary Fermi gases Boettcher, I.; Braun, J.; Herbst, T. K. Physical Review A, Vol. 91, Issue 1 https://doi.org/10.1103/PhysRevA.91.013610	journal	January 2015
The QCD equation of state from the lattice Philipsen, Owe Progress in Particle and Nuclear Physics, Vol. 70 https://doi.org/10.1016/j.ppnp.2012.09.003	journal	May 2013
Gauge cooling in complex Langevin for lattice QCD with heavy quarks Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu Physics Letters B, Vol. 723, Issue 1-3 https://doi.org/10.1016/j.physletb.2013.04.062	journal	June 2013
Reweighting Lefschetz Thimbles Bluecher, Stefan; Pawlowski, Jan M.; Scherzer, Manuel SciPost Physics, Vol. 5, Issue 5 https://doi.org/10.21468/SciPostPhys.5.5.044	journal	January 2018
The QCD phase diagram at nonzero quark density Endrődi, G.; Fodor, Z.; Katz, S. D. Journal of High Energy Physics, Vol. 2011, Issue 4 https://doi.org/10.1007/JHEP04(2011)001	journal	April 2011
Minkowski stochastic quantization Nakazato, Hiromichi; Yamanaka, Yoshiya Physical Review D, Vol. 34, Issue 2 https://doi.org/10.1103/PhysRevD.34.492	journal	July 1986
A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models Motome, Yukitoshi; Imada, Masatoshi Journal of the Physical Society of Japan, Vol. 66, Issue 7 https://doi.org/10.1143/JPSJ.66.1872	journal	July 1997
Complex coacervation: A field theoretic simulation study of polyelectrolyte complexation Lee, Jonghoon; Popov, Yuri O.; Fredrickson, Glenn H. The Journal of Chemical Physics, Vol. 128, Issue 22 https://doi.org/10.1063/1.2936834	journal	June 2008
Langevin simulations of lattice field theories Batrouni, G. G.; Katz, G. R.; Kronfeld, A. S. Physical Review D, Vol. 32, Issue 10 https://doi.org/10.1103/PhysRevD.32.2736	journal	November 1985
A numerical attempt on the chiral Schwinger model Kieu, T. D.; Hawkins, P. S. Nuclear Physics B - Proceedings Supplements, Vol. 42, Issue 1-3 https://doi.org/10.1016/0920-5632(95)00330-C	journal	April 1995
Developing and testing the density of states FFA method in the SU(3) spin model Giuliani, Mario; Gattringer, Christof; Törek, Pascal Nuclear Physics B, Vol. 913 https://doi.org/10.1016/j.nuclphysb.2016.10.005	journal	December 2016
Stochastic quantization Damgaard, Poul H.; Hüffel, Helmuth Physics Reports, Vol. 152, Issue 5-6 https://doi.org/10.1016/0370-1573(87)90144-X	journal	August 1987
Meron-Cluster Solution of Fermion Sign Problems Chandrasekharan, Shailesh; Wiese, Uwe-Jens Physical Review Letters, Vol. 83, Issue 16 https://doi.org/10.1103/PhysRevLett.83.3116	journal	October 1999
Continuous time Monte Carlo for lattice QCD in the strong coupling limit Unger, W.; de Forcrand, Ph Journal of Physics G: Nuclear and Particle Physics, Vol. 38, Issue 12 https://doi.org/10.1088/0954-3899/38/12/124190	journal	November 2011
Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)073	journal	July 2016
Solutions to sign problems in lattice Yukawa models Chandrasekharan, Shailesh Physical Review D, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevD.86.021701	journal	July 2012
Complex Langevin dynamics in large $N$ unitary matrix models Basu, Pallab; Jaswin, Kasi; Joseph, Anosh Physical Review D, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevD.98.034501	journal	August 2018
Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases Frank, B.; Lang, J.; Zwerger, W. Journal of Experimental and Theoretical Physics, Vol. 127, Issue 5 https://doi.org/10.1134/S1063776118110031	journal	November 2018
Complex saddle points and the sign problem in complex Langevin simulation Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya Nuclear Physics B, Vol. 911 https://doi.org/10.1016/j.nuclphysb.2016.07.031	journal	October 2016
Coherent-state Langevin equations for canonical quantum systems with applications to the quantized Hall effect Klauder, John R. Physical Review A, Vol. 29, Issue 4 https://doi.org/10.1103/PhysRevA.29.2036	journal	April 1984
Finite density ${QED}_{1 + 1}$ near Lefschetz thimbles Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F. Physical Review D, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevD.98.034506	journal	August 2018
Justification of the complex Langevin method with the gauge cooling procedure Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 1 https://doi.org/10.1093/ptep/ptv173	journal	January 2016
Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases Liu, Xia-Ji Physics Reports, Vol. 524, Issue 2 https://doi.org/10.1016/j.physrep.2012.10.004	journal	March 2013
Path integral contour deformations for noisy observables Detmold, William; Kanwar, Gurtej; Wagman, Michael L. Physical Review D, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevD.102.014514	journal	July 2020
Finite size effects in the presence of a chemical potential: A study in the classical nonlinear $O (2)$ sigma model Banerjee, Debasish; Chandrasekharan, Shailesh Physical Review D, Vol. 81, Issue 12 https://doi.org/10.1103/PhysRevD.81.125007	journal	June 2010
Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions Chandrasekharan, Shailesh; Li, Anyi Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)018	journal	January 2011
Realization of a Strongly Interacting Bose-Fermi Mixture from a Two-Component Fermi Gas Shin, Yong-il; Schirotzek, André; Schunck, Christian H. Physical Review Letters, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevLett.101.070404	journal	August 2008
Sign problem in the numerical simulation of many-electron systems Loh, E. Y.; Gubernatis, J. E.; Scalettar, R. T. Physical Review B, Vol. 41, Issue 13 https://doi.org/10.1103/PhysRevB.41.9301	journal	May 1990
Complex Langevin simulations of a finite density matrix model for QCD Bloch, Jacques; Glesaaen, Jonas; Philipsen, Owe EPJ Web of Conferences, Vol. 137 https://doi.org/10.1051/epjconf/201713707030	journal	January 2017
Canonical partition function and finite density phase transition in lattice QCD Ejiri, Shinji Physical Review D, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevD.78.074507	journal	October 2008
Ground-state energy of spin- $\frac{1}{2}$ fermions in the unitary limit Lee, Dean Physical Review B, Vol. 73, Issue 11 https://doi.org/10.1103/PhysRevB.73.115112	journal	March 2006
Stochastic quantization in Minkowski space Hüffel, H.; Rumpf, H. Physics Letters B, Vol. 148, Issue 1-3 https://doi.org/10.1016/0370-2693(84)91619-8	journal	November 1984
Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model Assaad, F. F. Physical Review Letters, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevLett.83.796	journal	July 1999
Flux representation of an effective Polyakov loop model for QCD thermodynamics Gattringer, Christof Nuclear Physics B, Vol. 850, Issue 2 https://doi.org/10.1016/j.nuclphysb.2011.04.018	journal	September 2011
Parallel tempering algorithm for integration over Lefschetz thimbles Fukuma, Masafumi; Umeda, Naoya Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 7 https://doi.org/10.1093/ptep/ptx081	journal	July 2017
Schwinger–Dyson equations and line integrals Salcedo, Lorenzo Luis; Seiler, Erhard Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 3 https://doi.org/10.1088/1751-8121/aaefca	journal	December 2018
Density of states and Fisher’s zeros in compact $U (1)$ pure gauge theory Bazavov, A.; Berg, B. A.; Du, Daping Physical Review D, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevD.85.056010	journal	March 2012
Simulating the all-order strong coupling expansion IV: as a loop model Wolff, Ulli Nuclear Physics B, Vol. 832, Issue 3 https://doi.org/10.1016/j.nuclphysb.2010.02.005	journal	June 2010
Abelian gauge theories on the lattice: θ-Terms and compact gauge theory with(out) monopoles Sulejmanpasic, Tin; Gattringer, Christof Nuclear Physics B, Vol. 943 https://doi.org/10.1016/j.nuclphysb.2019.114616	journal	June 2019
Gauge theories with imaginary chemical potential and the phases of QCD Roberge, André; Weiss, Nathan Nuclear Physics B, Vol. 275, Issue 4 https://doi.org/10.1016/0550-3213(86)90582-1	journal	December 1986
Shell model Monte Carlo methods Koonin, S. E.; Dean, D. J.; Langanke, K. Physics Reports, Vol. 278, Issue 1 https://doi.org/10.1016/S0370-1573(96)00017-8	journal	January 1997
Complex Probabilities on $R^{N}$ as Real Probabilities on $C^{N}$ and an Application to Path Integrals Weingarten, Don Physical Review Letters, Vol. 89, Issue 24 https://doi.org/10.1103/PhysRevLett.89.240201	journal	November 2002
Lattice methods for strongly interacting many-body systems Drut, Joaquín E.; Nicholson, Amy N. Journal of Physics G: Nuclear and Particle Physics, Vol. 40, Issue 4 https://doi.org/10.1088/0954-3899/40/4/043101	journal	March 2013
Complex Langevin in Lattice QCD: Dynamic Stabilisation and the Phase Diagram Aarts, G.; Attanasio, F.; Jäger, B. Acta Physica Polonica B Proceedings Supplement, Vol. 9, Issue 3 https://doi.org/10.5506/APhysPolBSupp.9.621	journal	January 2016
Coupled-cluster computations of atomic nuclei Hagen, G.; Papenbrock, T.; Hjorth-Jensen, M. Reports on Progress in Physics, Vol. 77, Issue 9 https://doi.org/10.1088/0034-4885/77/9/096302	journal	September 2014
Chiral phase transition in two-flavor QCD from an imaginary chemical potential Bonati, Claudio; de Forcrand, Philippe; D’Elia, Massimo Physical Review D, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevD.90.074030	journal	October 2014
The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant Ito, Yuta; Nishimura, Jun Journal of High Energy Physics, Vol. 2016, Issue 12 https://doi.org/10.1007/JHEP12(2016)009	journal	December 2016
Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices and particle-partition entanglement Rammelmüller, Lukas; Porter, William J.; Braun, Jens Physical Review A, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevA.96.033635	journal	September 2017
Inhomogeneous chiral condensates Buballa, Michael; Carignano, Stefano Progress in Particle and Nuclear Physics, Vol. 81 https://doi.org/10.1016/j.ppnp.2014.11.001	journal	March 2015
Numerical study of unitary fermions in one spatial dimension Endres, Michael G. Physical Review A, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevA.87.063617	journal	June 2013
Positive representations of a class of complex measures Seiler, Erhard; Wosiek, Jacek Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 49 https://doi.org/10.1088/1751-8121/aa9310	journal	November 2017
Restricted phase-space approximation in real-time stochastic quantization Anzaki, Ryoji; Fukushima, Kenji; Hidaka, Yoshimasa Annals of Physics, Vol. 353 https://doi.org/10.1016/j.aop.2014.11.004	journal	February 2015
Reliability of Taylor expansions in QCD Brandt, B. B.; Endrődi, G. Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevD.99.014518	journal	January 2019
Numerical problems in applying the langevin equation to complex effective actions Ambjørn, Jan; Yang, S. -K. Physics Letters B, Vol. 165, Issue 1-3 https://doi.org/10.1016/0370-2693(85)90708-7	journal	December 1985
Complex reaction noise in a molecular quasispecies model Hochberg, David; Zorzano, María-Paz; Morán, Federico Chemical Physics Letters, Vol. 423, Issue 1-3 https://doi.org/10.1016/j.cplett.2006.03.023	journal	May 2006
Complex Langevin equations and Schwinger–Dyson equations Guralnik, Gerald; Pehlevan, Cengiz Nuclear Physics B, Vol. 811, Issue 3 https://doi.org/10.1016/j.nuclphysb.2008.11.034	journal	April 2009
Equation of state of the unitary Fermi gas: An update on lattice calculations Drut, Joaquín E.; Lähde, Timo A.; Wlazłowski, Gabriel Physical Review A, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevA.85.051601	journal	May 2012
Simulating the all-order strong coupling expansion III: <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mtext>O</mml:mtext><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> sigma/loop models Wolff, Ulli Nuclear Physics B, Vol. 824, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2009.09.006	journal	January 2010
Solution to sign problems in half-filled spin-polarized electronic systems Huffman, Emilie Fulton; Chandrasekharan, Shailesh Physical Review B, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevB.89.111101	journal	March 2014
Complex Langevin simulation of quantum vortices in a Bose-Einstein condensate Hayata, Tomoya; Yamamoto, Arata Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.043628	journal	October 2015
Simulating the all-order hopping expansion II: Wilson fermions Wolff, Ulli Nuclear Physics B, Vol. 814, Issue 3 https://doi.org/10.1016/j.nuclphysb.2009.01.018	journal	June 2009
Existence of the critical point in finite density lattice QCD Ejiri, Shinji Physical Review D, Vol. 77, Issue 1 https://doi.org/10.1103/PhysRevD.77.014508	journal	January 2008
Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.241117	journal	June 2015
Fermion-induced quantum critical points Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00167-6	journal	August 2017
Method for simulating $O (N)$ lattice models at finite density Endres, Michael G. Physical Review D, Vol. 75, Issue 6 https://doi.org/10.1103/PhysRevD.75.065012	journal	March 2007
The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems Strinati, Giancarlo Calvanese; Pieri, Pierbiagio; Röpke, Gerd Physics Reports, Vol. 738 https://doi.org/10.1016/j.physrep.2018.02.004	journal	April 2018
Stability of complex Langevin dynamics in effective models Aarts, Gert; James, Frank A.; Pawlowski, Jan M. Journal of High Energy Physics, Vol. 2013, Issue 3 https://doi.org/10.1007/JHEP03(2013)073	journal	March 2013
Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation Mercado, Ydalia Delgado; Gattringer, Christof Nuclear Physics B, Vol. 862, Issue 3 https://doi.org/10.1016/j.nuclphysb.2012.05.009	journal	September 2012
Complex Langevin calculations in finite density QCD at large $μ / T$ with the deformation technique Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji Physical Review D, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevD.98.114513	journal	December 2018
Fermions at Finite Density in $2 + 1$ Dimensions with Sign-Optimized Manifolds Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry Physical Review Letters, Vol. 121, Issue 19 https://doi.org/10.1103/PhysRevLett.121.191602	journal	November 2018
Lattice QCD with fermions at strong coupling: A dimer system Rossi, Pietro; Wolff, Ulli Nuclear Physics B, Vol. 248, Issue 1 https://doi.org/10.1016/0550-3213(84)90589-3	journal	December 1984
On complex probabilities Parisi, Giorgio Physics Letters B, Vol. 131, Issue 4-6 https://doi.org/10.1016/0370-2693(83)90525-7	journal	November 1983
Complex Langevin equation and the many-fermion problem Adami, Chris; Koonin, Steven E. Physical Review C, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevC.63.034319	journal	February 2001
QCD Crossover at Finite Chemical Potential from Lattice Simulations Borsanyi, Szabolcs; Fodor, Zoltan; Guenther, Jana N. Physical Review Letters, Vol. 125, Issue 5 https://doi.org/10.1103/PhysRevLett.125.052001	journal	July 2020
On the stochastic quantization of field theory Jona-Lasinio, G.; Mitter, P. K. Communications in Mathematical Physics, Vol. 101, Issue 3 https://doi.org/10.1007/BF01216097	journal	September 1985
Density of States FFA analysis of SU(3) lattice gauge theory at a finite density of color sources Giuliani, Mario; Gattringer, Christof Physics Letters B, Vol. 773 https://doi.org/10.1016/j.physletb.2017.08.014	journal	October 2017
Fermion sign problem: Decoupling transformation and simulation algorithm Batrouni, Ghassan George; de Forcrand, Philippe Physical Review B, Vol. 48, Issue 1 https://doi.org/10.1103/PhysRevB.48.589	journal	July 1993
Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations Wei, Z. C.; Wu, Congjun; Li, Yi Physical Review Letters, Vol. 116, Issue 25 https://doi.org/10.1103/PhysRevLett.116.250601	journal	June 2016
Equilibrium limit of the stochastic quantization in minkowski space Fukuda, R.; Higurashi, H. Physics Letters B, Vol. 202, Issue 4 https://doi.org/10.1016/0370-2693(88)91861-8	journal	March 1988
Testing the criterion for correct convergence in the complex Langevin method Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/JHEP05(2018)004	journal	May 2018
Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models Anagnostopoulos, Konstantinos N.; Azuma, Takehiro; Ito, Yuta Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)151	journal	February 2018
Lattice QCD at Finite Density: An Introductory Review Muroya, S.; Nakamura, A.; Nonaka, C. Progress of Theoretical Physics, Vol. 110, Issue 4 https://doi.org/10.1143/PTP.110.615	journal	October 2003
New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble Cristoforetti, Marco; Di Renzo, Francesco; Scorzato, Luigi Physical Review D, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevD.86.074506	journal	October 2012
$N_{f} = 2$ QCD chiral phase transition with Wilson fermions at zero and imaginary chemical potential Philipsen, Owe; Pinke, Christopher Physical Review D, Vol. 93, Issue 11 https://doi.org/10.1103/PhysRevD.93.114507	journal	June 2016
Ground state energy at unitarity Lee, Dean Physical Review C, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevC.78.024001	journal	August 2008
Baryon bags in strong coupling QCD Gattringer, Christof Physical Review D, Vol. 97, Issue 7 https://doi.org/10.1103/PhysRevD.97.074506	journal	April 2018
Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas Aarts, Gert Journal of High Energy Physics, Vol. 2009, Issue 05 https://doi.org/10.1088/1126-6708/2009/05/052	journal	May 2009
A simple approach towards the sign problem using path optimisation Bursa, Francis; Kroyter, Michael Journal of High Energy Physics, Vol. 2018, Issue 12 https://doi.org/10.1007/JHEP12(2018)054	journal	December 2018
The mechanism of complex Langevin simulations Gausterer, H.; Lee, Sean Journal of Statistical Physics, Vol. 73, Issue 1-2 https://doi.org/10.1007/BF01052754	journal	October 1993
Stochastic quantization of Einstein gravity Rumpf, Helmut Physical Review D, Vol. 33, Issue 4 https://doi.org/10.1103/PhysRevD.33.942	journal	February 1986
Feynman diagrams versus Fermi-gas Feynman emulator Van Houcke, K.; Werner, F.; Kozik, E. Nature Physics, Vol. 8, Issue 5 https://doi.org/10.1038/nphys2273	journal	March 2012
The shell model Monte Carlo approach to level densities: recent developments and perspectives Alhassid, Y. arXiv https://doi.org/10.48550/arxiv.1601.00107	text	January 2016
Spin and charge dynamics of the ferromagnetic and antiferromagnetic two-dimensional half-filled Kondo lattice model Capponi, S.; Assaad, F. F. arXiv https://doi.org/10.48550/arxiv.cond-mat/0010393	text	January 2000
Charge and Spin Structures of a $d_{x^2 - y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator Assaad, F. F.; Imada, M.; Scalapino, D. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/9706173	text	January 1997
Quantum Monte Carlo simulations of the half-filled two-dimensional Kondo lattice model Assaad, F. F. arXiv https://doi.org/10.48550/arxiv.cond-mat/9904178	text	January 1999

Similar Records

Going with the flow: a new solution to the sign problem

Journal Article · Mon Sep 25 00:00:00 EDT 2017 · Nuclear Physics. A · OSTI ID:1850142

Başar, Gökçe

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

Journal Article · Tue May 10 00:00:00 EDT 2016 · Journal of High Energy Physics (Online) · OSTI ID:1850142

Alexandru, Andrei; Basar, Gokce; Bedaque, Paulo F.; +2 more

Machine learning to alleviate Hubbard-model sign problems

Journal Article · Thu Mar 25 00:00:00 EDT 2021 · Physical Review. B · OSTI ID:1850142

Wynen, Jan-Lukas; Berkowitz, Evan; Krieg, Stefan; +2 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
Sign problem
Stochastic quantization
Complex Langevin

Title: Complex Langevin and other approaches to the sign problem in quantum many-body physics

Citation Formats

References (307)

Similar Records

Related Subjects