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

Abstract

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.

Authors:
; ;
Publication Date:
Research Org.:
Duke Univ., Durham, NC (United States); Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1423715
Alternate Identifier(s):
OSTI ID: 1498953
Grant/Contract Number:  
FG02-05ER41368; SC0010005
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 5; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Ayyar, Venkitesh, Chandrasekharan, Shailesh, and Rantaharju, Jarno. Benchmark results in the 2D lattice Thirring model with a chemical potential. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.054501.
Ayyar, Venkitesh, Chandrasekharan, Shailesh, & Rantaharju, Jarno. Benchmark results in the 2D lattice Thirring model with a chemical potential. United States. doi:10.1103/PhysRevD.97.054501.
Ayyar, Venkitesh, Chandrasekharan, Shailesh, and Rantaharju, Jarno. Mon . "Benchmark results in the 2D lattice Thirring model with a chemical potential". United States. doi:10.1103/PhysRevD.97.054501.
@article{osti_1423715,
title = {Benchmark results in the 2D lattice Thirring model with a chemical potential},
author = {Ayyar, Venkitesh and Chandrasekharan, Shailesh and Rantaharju, Jarno},
abstractNote = {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.},
doi = {10.1103/PhysRevD.97.054501},
journal = {Physical Review D},
number = 5,
volume = 97,
place = {United States},
year = {2018},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.054501

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Cited by: 2 works
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Works referenced in this record:

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

  • Alexandru, Andrei; Basar, Gökçe; Bedaque, Paulo F.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)053

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

  • Aarts, Gert; Attanasio, Felipe; Jäger, Benjamin
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)087

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

  • Aarts, Gert; Seiler, Erhard; Sexty, Dénes
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)044

Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density
journal, September 2016

  • Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)172

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

  • Cristoforetti, Marco; Di Renzo, Francesco; Mukherjee, Abhishek
  • Physical Review D, Vol. 88, Issue 5
  • DOI: 10.1103/PhysRevD.88.051501

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

  • Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)125

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