Solution to sign problems in models of interacting fermions and quantum spins
Abstract
We show that solutions to fermion sign problems that are found in the formulation where the path integral is expanded in powers of the interaction in continuous time can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the world-line representation of quantum spins. Combining this idea with meron-cluster methods, we are able to further extend the class of models that are solvable. We demonstrate these solutions to sign problems by considering several examples of strongly correlated systems that contain the physics of semimetals, insulators, superfluidity, and antiferromagnetism.
- Authors:
-
- Duke Univ., Durham, NC (United States). Dept. of Physics
- Duke Univ., Durham, NC (United States). Dept. of Physics; Indian Inst. of Science, Bangalore (India). Center for High Energy Physics
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1536400
- Alternate Identifier(s):
- OSTI ID: 1329344
- Grant/Contract Number:
- FG02-05ER41368
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 4; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Huffman, Emilie, and Chandrasekharan, Shailesh. Solution to sign problems in models of interacting fermions and quantum spins. United States: N. p., 2016.
Web. doi:10.1103/physreve.94.043311.
Huffman, Emilie, & Chandrasekharan, Shailesh. Solution to sign problems in models of interacting fermions and quantum spins. United States. https://doi.org/10.1103/physreve.94.043311
Huffman, Emilie, and Chandrasekharan, Shailesh. Wed .
"Solution to sign problems in models of interacting fermions and quantum spins". United States. https://doi.org/10.1103/physreve.94.043311. https://www.osti.gov/servlets/purl/1536400.
@article{osti_1536400,
title = {Solution to sign problems in models of interacting fermions and quantum spins},
author = {Huffman, Emilie and Chandrasekharan, Shailesh},
abstractNote = {We show that solutions to fermion sign problems that are found in the formulation where the path integral is expanded in powers of the interaction in continuous time can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the world-line representation of quantum spins. Combining this idea with meron-cluster methods, we are able to further extend the class of models that are solvable. We demonstrate these solutions to sign problems by considering several examples of strongly correlated systems that contain the physics of semimetals, insulators, superfluidity, and antiferromagnetism.},
doi = {10.1103/physreve.94.043311},
journal = {Physical Review E},
number = 4,
volume = 94,
place = {United States},
year = {Wed Oct 19 00:00:00 EDT 2016},
month = {Wed Oct 19 00:00:00 EDT 2016}
}
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Works referenced in this record:
From spin ladders to the 2D O(3) model at non-zero density
journal, August 2002
- Chandrasekharan, S.; Scarlet, B.; Wiese, U. -J.
- Computer Physics Communications, Vol. 147, Issue 1-2
Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations
journal, September 2006
- Boninsegni, M.; Prokof’ev, N. V.; Svistunov, B. V.
- Physical Review E, Vol. 74, Issue 3
Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation
journal, June 2015
- Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
- Physical Review B, Vol. 91, Issue 24
Efficient continuous-time quantum Monte Carlo algorithm for fermionic lattice models
journal, June 2015
- Iazzi, Mauro; Troyer, Matthias
- Physical Review B, Vol. 91, Issue 24
Real-time simulation of nonequilibrium transport of magnetization in large open quantum spin systems driven by dissipation
journal, September 2015
- Banerjee, D.; Hebenstreit, F.; Jiang, F. -J.
- Physical Review B, Vol. 92, Issue 12
Efficient continuous-time quantum Monte Carlo method for the ground state of correlated fermions
journal, June 2015
- Wang, Lei; Iazzi, Mauro; Corboz, Philippe
- Physical Review B, Vol. 91, Issue 23
Fermion bag solutions to some sign problems in four-fermion field theories
journal, May 2012
- Chandrasekharan, Shailesh; Li, Anyi
- Physical Review D, Vol. 85, Issue 9
Generalized directed loop method for quantum Monte Carlo simulations
journal, March 2005
- Alet, Fabien; Wessel, Stefan; Troyer, Matthias
- Physical Review E, Vol. 71, Issue 3
Fermion bag approach to fermion sign problems: New opportunities in lattice fermion field theories
journal, July 2013
- Chandrasekharan, Shailesh
- The European Physical Journal A, Vol. 49, Issue 7
Real-time dynamics of open quantum spin systems driven by dissipative processes
journal, July 2015
- Hebenstreit, F.; Banerjee, D.; Hornung, M.
- Physical Review B, Vol. 92, Issue 3
Origin of fermion masses without spontaneous symmetry breaking
journal, April 2016
- Ayyar, Venkitesh; Chandrasekharan, Shailesh
- Physical Review D, Vol. 93, Issue 8
Quantum Monte Carlo Simulations of the Half-Filled Two-Dimensional Kondo Lattice Model
journal, July 1999
- Assaad, F. F.
- Physical Review Letters, Vol. 83, Issue 4
Continuous-time Monte Carlo methods for quantum impurity models
journal, May 2011
- Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I.
- Reviews of Modern Physics, Vol. 83, Issue 2
Quantum Monte Carlo with directed loops
journal, October 2002
- Syljuåsen, Olav F.; Sandvik, Anders W.
- Physical Review E, Vol. 66, Issue 4
Fermion Bags, Duality, and the Three Dimensional Massless Lattice Thirring Model
journal, April 2012
- Chandrasekharan, Shailesh; Li, Anyi
- Physical Review Letters, Vol. 108, Issue 14
Numerical study of dense adjoint matter in two color QCD
journal, October 2000
- Hands, S.; Montvay, I.; Morrison, S.
- The European Physical Journal C, Vol. 17, Issue 2
Simulations of Discrete Quantum Systems in Continuous Euclidean Time
journal, December 1996
- Beard, B. B.; Wiese, U. -J.
- Physical Review Letters, Vol. 77, Issue 25
Lattice simulations for few- and many-body systems
journal, July 2009
- Lee, Dean
- Progress in Particle and Nuclear Physics, Vol. 63, Issue 1
Fermion-dimer scattering using an impurity lattice Monte Carlo approach and the adiabatic projection method
journal, December 2014
- Elhatisari, Serdar; Lee, Dean
- Physical Review C, Vol. 90, Issue 6
Real-time simulation of large open quantum spin systems driven by dissipation
journal, December 2014
- Banerjee, D.; Jiang, F. -J.; Kon, M.
- Physical Review B, Vol. 90, Issue 24
Polaron Problem by Diagrammatic Quantum Monte Carlo
journal, September 1998
- Prokof'ev, Nikolai V.; Svistunov, Boris V.
- Physical Review Letters, Vol. 81, Issue 12
Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
journal, August 2015
- Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
- New Journal of Physics, Vol. 17, Issue 8
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
journal, October 2014
- Wang, Lei; Corboz, Philippe; Troyer, Matthias
- New Journal of Physics, Vol. 16, Issue 10
Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations
journal, June 2016
- Wei, Z. C.; Wu, Congjun; Li, Yi
- Physical Review Letters, Vol. 116, Issue 25
Kondo Bosons and the Kondo Lattice: Microscopic Basis for the Heavy Fermi Liquid
journal, August 1986
- Auerbach, Assa; Levin, K.
- Physical Review Letters, Vol. 57, Issue 7
Critical Temperature Curve in BEC-BCS Crossover
journal, August 2008
- Burovski, Evgeni; Kozik, Evgeny; Prokof’ev, Nikolay
- Physical Review Letters, Vol. 101, Issue 9
Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981
- Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review D, Vol. 24, Issue 8
Meron-Cluster Solution of Fermion Sign Problems
journal, October 1999
- Chandrasekharan, Shailesh; Wiese, Uwe-Jens
- Physical Review Letters, Vol. 83, Issue 16
Evading the Sign Problem in Random Matrix Simulations
journal, September 2011
- Bloch, Jacques
- Physical Review Letters, Vol. 107, Issue 13
Lattice methods for strongly interacting many-body systems
journal, March 2013
- Drut, Joaquín E.; Nicholson, Amy N.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 40, Issue 4
Continuous-time quantum Monte Carlo method for fermions
journal, July 2005
- Rubtsov, A. N.; Savkin, V. V.; Lichtenstein, A. I.
- Physical Review B, Vol. 72, Issue 3
Solution of the complex action problem in the Potts model for dense QCD
journal, May 2001
- Alford, M.; Chandrasekharan, S.; Cox, J.
- Nuclear Physics B, Vol. 602, Issue 1-2
Solutions to sign problems in lattice Yukawa models
journal, July 2012
- Chandrasekharan, Shailesh
- Physical Review D, Vol. 86, Issue 2
Meron-Cluster Simulation of the Vacuum in the 2D O(3) Model
journal, December 1995
- Bietenholz, W.; Pochinsky, A.; Wiese, U. -J.
- Physical Review Letters, Vol. 75, Issue 24
Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome
journal, December 2007
- Prokof’ev, Nikolay; Svistunov, Boris
- Physical Review Letters, Vol. 99, Issue 25
Fermion bag approach to lattice field theories
journal, July 2010
- Chandrasekharan, Shailesh
- Physical Review D, Vol. 82, Issue 2
Solution to sign problems in half-filled spin-polarized electronic systems
journal, March 2014
- Huffman, Emilie Fulton; Chandrasekharan, Shailesh
- Physical Review B, Vol. 89, Issue 11
Bold diagrammatic Monte Carlo: A generic sign-problem tolerant technique for polaron models and possibly interacting many-body problems
journal, March 2008
- Prokof’ev, N. V.; Svistunov, B. V.
- Physical Review B, Vol. 77, Issue 12
Worm Algorithms for Classical Statistical Models
journal, September 2001
- Prokof'ev, Nikolay; Svistunov, Boris
- Physical Review Letters, Vol. 87, Issue 16
Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity
journal, November 2010
- Goulko, Olga; Wingate, Matthew
- Physical Review A, Vol. 82, Issue 5
Simulations of discrete quantum systems in continuous euclidean time
journal, February 1997
- Beard, B. B.; Wiese, U. -J.
- Nuclear Physics B - Proceedings Supplements, Vol. 53, Issue 1-3
Lattice methods for strongly interacting many-body systems
text, January 2013
- Joaquín, Drut,; Amy, Nicholson,
- The University of North Carolina at Chapel Hill University Libraries
Evading the sign problem in random matrix simulations
conference, July 2012
- Bloch, Jacques
- Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)
Worm Algorithms for Classical Statistical Models
text, January 2001
- Prokofev, Nikolay; Svistunov, Boris
- The American Physical Society
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
text, January 2014
- Wang, Lei; Corboz, Philippe; Troyer, Matthias
- ETH Zurich
Real-time simulation of large open quantum spin systems driven by dissipation
text, January 2014
- Wiese, Uwe-Jens; Jiang, F. -J.; Banerjee, Debasish
- American Physical Society
The fermion bag approach to lattice field theories
text, January 2009
- Chandrasekharan, Shailesh
- arXiv
Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity
text, January 2010
- Goulko, Olga; Wingate, Matthew
- arXiv
Fermion bags, duality and the three dimensional massless lattice Thirring model
text, January 2011
- Chandrasekharan, Shailesh; Li, Anyi
- arXiv
Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
text, January 2014
- Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
- arXiv
Real-time dynamics of open quantum spin systems driven by dissipative processes
text, January 2015
- Hebenstreit, Florian; Banerjee, Debasish; Hornung, Manes
- arXiv
Origin of fermion masses without spontaneous symmetry breaking
text, January 2015
- Ayyar, Venkitesh; Chandrasekharan, Shailesh
- arXiv
Majorana Positivity and the Fermion sign problem of Quantum Monte Carlo Simulations
text, January 2016
- Wei, Z. C.; Wu, Congjun; Li, Yi
- arXiv
Generalized Directed Loop Method for Quantum Monte Carlo Simulations
text, January 2003
- Alet, Fabien; Wessel, Stefan; Troyer, Matthias
- arXiv
Meron-Cluster Solution of Fermion Sign Problems
text, January 1999
- Chandrasekharan, Shailesh; Wiese, Uwe-Jens
- arXiv
From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
text, January 2001
- Chandrasekharan, S.; Scarlet, B.; Wiese, U. -J.
- arXiv
Works referencing / citing this record:
Phase space methods for Majorana fermions
journal, May 2018
- Joseph, Ria Rushin; Rosales-Zárate, Laura E. C.; Drummond, Peter D.
- Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 24
Alleviating the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multiorbital Hubbard models
journal, January 2020
- Kim, Aaram J.; Werner, Philipp; Valentí, Roser
- Physical Review B, Vol. 101, Issue 4