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

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.