Comparison between Fermion Bag Approach and Complex Langevin Dynamics for Massive Thirring Model at Finite Density in 0 + 1 Dimensions

TL;DR

This paper compares the fermion bag approach and complex Langevin dynamics for solving the sign problem in the 0+1 dimensional massive Thirring model at finite density, highlighting the fermion bag approach's advantages.

Contribution

It introduces and compares the fermion bag approach with Langevin methods, demonstrating its effectiveness in avoiding the sign problem in this model.

Findings

Fermion bag approach and Langevin dynamics avoid the sign problem.

Fermion density and chiral condensate match exact results.

Fermion bag approach shows advantages over Langevin methods.

Abstract

We consider the massive Thirring model at finite density in 0+1 dimension. The fermion bag approach, Langevin dynamics and complex Langevin dynamics are adopted to attack the sign problem for this model. Compared with the complex Langevin dynamics, both fermion bag approach and Langvin dynamics avoid the sign problem. The fermion density and chiral condensate, which are obtained by these numerical methods, are compared with the exact results. The advantages of the fermion bag approach over the other numerical methods are also discussed.