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 po- tential. Our model is asymptotically free, 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.

arXiv comment11 pages, 13 figures, 7 tables

References in corpus (30)

• Quantum Monte Carlo with Directed Loops
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Worm algorithms for classical statistical models
• High density QCD on a Lefschetz thimble?
• The Loop Algorithm
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• The Square-Lattice Heisenberg Antiferromagnet at Very Large Correlation Lengths
• New insights into the problem with a singular drift term in the complex Langevin method
• The fermion bag approach to lattice field theories
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Complex Langevin dynamics and zeroes of the fermion determinant
• Deep Learning Beyond Lefschetz Thimbles
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Origin of fermion masses without spontaneous symmetry breaking
• On the convergence of complex Langevin dynamics: the three-dimensional XY model at finite chemical potential
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• The Three Dimensional Thirring Model for Small N_f
• Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model
• Monte Carlo calculations of the finite density Thirring model
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics
• Cluster simulation of relativistic fermions in two space-time dimensions
• Monte Carlo Simulation of the Three Dimensional Thirring Model
• Thirring model at finite density in 2+1 dimensions with stochastic quantization
• Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories
• Fermion loop simulation of the lattice Gross-Neveu model
• Complex Langevin simulations of a finite density matrix model for QCD
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• Absence of vortex condensation in a two dimensional fermionic XY model

Cited by in corpus (11)

• Review on novel methods for lattice gauge theories
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• Few-body physics on a space-time lattice in the worldline approach
• Improved coarse-graining methods on two dimensional tensor networks including fermions
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Baryon bags in strong coupling QCD
• Crystalline phases at finite winding densities in a quantum link ladder
• Fermion Bag Approach for Hamiltonian Lattice Field Theories
• Finite density 2d O(3) sigma model: dualization and numerical simulations
• Abelian color cycle and abelian color flux dualization methods for non-abelian lattice field theories