skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Benchmark results in the 2D lattice Thirring model with a chemical potential

Journal Article · · Physical Review. D.
; ;

We study the two-dimensional lattice Thirring model in the presence of a fermion chemical potential. Our model is asymptotically free and contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence, it is a useful toy model for QCD, especially since it, too, suffers from a sign problem in the auxiliary field formulation in the presence of a fermion chemical potential. In this work, we formulate the model in both the world line and fermion-bag representations and show that the sign problem can be completely eliminated with open boundary conditions when the fermions are massless. Hence, we are able accurately compute a variety of interesting quantities in the model, and these results could provide benchmarks for other methods that are being developed to solve the sign problem in QCD.

Research Organization:
Duke Univ., Durham, NC (United States); Univ. of Colorado, Boulder, CO (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
FG02-05ER41368; SC0010005
OSTI ID:
1423715
Alternate ID(s):
OSTI ID: 1498953
Journal Information:
Physical Review. D., Journal Name: Physical Review. D. Vol. 97 Journal Issue: 5; ISSN 2470-0010
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

References (35)

Fermion-loop simulation of the lattice Gross-Neveu model journal July 2007
Chiral symmetry, the 1/N expansion and the SU(N) thirring model journal November 1978
Solving the sign problems of the massless lattice Schwinger model with a dual formulation journal August 2015
Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations journal September 2006
Lefschetz-thimble analysis of the sign problem in one-site fermion model journal March 2016
Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O ( 2 ) sigma model journal June 2010
Absence of vortex condensation in a two dimensional fermionic X Y model journal March 2008
On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential journal August 2010
Sign problem and Monte Carlo calculations beyond Lefschetz thimbles journal May 2016
Complex Langevin simulations of a finite density matrix model for QCD journal January 2017
Cluster simulation of relativistic fermions in two space–time dimensions journal January 2008
The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics journal September 2016
Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths journal February 1998
The loop algorithm journal January 2003
Lefschetz thimble Monte Carlo for many-body theories: A Hubbard model study journal July 2014
Deep learning beyond Lefschetz thimbles journal November 2017
Origin of fermion masses without spontaneous symmetry breaking journal April 2016
Monte Carlo calculations of the finite density Thirring model journal January 2017
Three-dimensional thirring model for small Nf journal September 1997
Quantum Monte Carlo with directed loops journal October 2002
Fermion Bags, Duality, and the Three Dimensional Massless Lattice Thirring Model journal April 2012
Complex Langevin dynamics and zeroes of the fermion determinant journal May 2017
Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density journal September 2016
Grand Canonical Ensembles, Multiparticle Wave Functions, Scattering Data, and Lattice Field Theories journal December 2015
Metropolis Monte Carlo integration on the Lefschetz thimble: Application to a one-plaquette model journal September 2013
Thirring model at finite density in 2 + 1 dimensions with stochastic quantization journal May 2013
Fermion bag approach for the massive Thirring model at finite density journal December 2016
Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem journal September 2013
Monte Carlo simulation of the three dimensional Thirring model journal April 1996
Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density journal December 2015
Quantum critical behavior in three dimensional lattice Gross-Neveu models journal July 2013
New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble journal October 2012
New insights into the problem with a singular drift term in the complex Langevin method journal July 2015
Fermion bag approach to lattice field theories journal July 2010
Worm Algorithms for Classical Statistical Models journal September 2001

Similar Records

Few-body physics on a spacetime lattice in the worldline approach
Journal Article · Wed Apr 24 00:00:00 EDT 2019 · Physical Review. D. · OSTI ID:1423715
Fermion bag approach to lattice field theories
Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields · OSTI ID:1423715
Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
Journal Article · Thu Mar 25 00:00:00 EDT 2021 · Physical Review D · OSTI ID:1423715

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS