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

TL;DR

This paper investigates the 2D lattice Thirring model with a chemical potential, demonstrating how to eliminate the sign problem in certain conditions, enabling accurate benchmarking for QCD-related studies.

Contribution

The study formulates the model in world line and fermion-bag representations, showing sign problem elimination with open boundary conditions for massless fermions.

Findings

Sign problem can be fully eliminated with open boundaries and massless fermions.

Accurate computation of physical quantities in the model.

Provides benchmarks for solving the sign problem in QCD.

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.