Finite-density Monte Carlo calculations on sign-optimized manifolds

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

doi:10.1103/PhysRevD.97.094510

Title: Finite-density Monte Carlo calculations on sign-optimized manifolds

Journal Article · Thu May 31 00:00:00 EDT 2018 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.97.094510· OSTI ID:1439896

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign (therefore reducing the sign problem) within a parametrized family of manifolds. We presents results for the 1 + 1 dimensional Thirring model with Wilson fermions on lattice sizes up to 40 × 10. This method reaches higher μ than previous techniques while substantially decreasing the computational time required.

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of Maryland, College Park, MD (United States); George Washington Univ., Washington, DC (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-95ER40907; FG02-93ER40762

OSTI ID:: 1439896

Alternate ID(s):: OSTI ID: 1498927

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Vol. 97 Journal Issue: 9; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 45 works

Citation information provided by
Web of Science

References (29)

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
Monte Carlo algorithm for simulating fermions on Lefschetz thimbles Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo Physical Review D, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevD.93.014504	journal	January 2016
Lefschetz-thimble analysis of the sign problem in one-site fermion model Tanizaki, Yuya; Hidaka, Yoshimasa; Hayata, Tomoya New Journal of Physics, Vol. 18, Issue 3 https://doi.org/10.1088/1367-2630/18/3/033002	journal	March 2016
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
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
QCD thermal phase transition in the presence of a small chemical potential Allton, C. R.; Ejiri, S.; Hands, S. J. Physical Review D, Vol. 66, Issue 7 https://doi.org/10.1103/PhysRevD.66.074507	journal	October 2002
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
Functional Integrals for QCD at Nonzero Chemical Potential and Zero Density Cohen, Thomas D. Physical Review Letters, Vol. 91, Issue 22 https://doi.org/10.1103/PhysRevLett.91.222001	journal	November 2003
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
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
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
Deep learning beyond Lefschetz thimbles Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry Physical Review D, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevD.96.094505	journal	November 2017
Multi-flavor massless QED2 at finite densities via Lefschetz thimbles Tanizaki, Yuya; Tachibana, Motoi Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)081	journal	February 2017
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
A new method to study lattice QCD at finite temperature and chemical potential Fodor, Z.; Katz, S. D. Physics Letters B, Vol. 534, Issue 1-4 https://doi.org/10.1016/S0370-2693(02)01583-6	journal	May 2002
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
Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)172	journal	September 2016
Thimble regularization at work: From toy models to chiral random matrix theories Di Renzo, F.; Eruzzi, G. Physical Review D, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevD.92.085030	journal	October 2015
Gauge and matter fields as surfaces and loops: An exploratory lattice study of the $Z_{3}$ gauge-Higgs model Gattringer, Christof; Schmidt, Alexander Physical Review D, Vol. 86, Issue 9 https://doi.org/10.1103/PhysRevD.86.094506	journal	November 2012
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
Finite density QCD with a canonical approach de Forcrand, Philippe; Kratochvila, Slavo Nuclear Physics B - Proceedings Supplements, Vol. 153, Issue 1 https://doi.org/10.1016/j.nuclphysbps.2006.01.007	journal	March 2006
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 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
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
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
Lattice QCD at finite density via a new canonical approach Alexandru, Andrei; Faber, Manfried; Horváth, Ivan Physical Review D, Vol. 72, Issue 11 https://doi.org/10.1103/PhysRevD.72.114513	journal	December 2005
Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo Physical Review D, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevD.94.045017	journal	August 2016
The chiral critical line of N _f = 2+1 QCD at zero and non-zero baryon density Forcrand, Philippe de; Philipsen, Owe Journal of High Energy Physics, Vol. 2007, Issue 01 https://doi.org/10.1088/1126-6708/2007/01/077	journal	January 2007
From the Density-of-states Method to Finite Density Quantum Field Theory Langfeld, K.; Lucini, B. Acta Physica Polonica B Proceedings Supplement, Vol. 9, Issue 3 https://doi.org/10.5506/APhysPolBSupp.9.503	journal	January 2016