Thirring model at finite density in2+1dimensions with stochastic quantization

Abstract

We consider a generalization of the Thirring model in 2+1 dimensions at finite density. We employ stochastic quantization and check for the applicability in the finite density case to circumvent the sign problem. To this end we derive analytical results in the heavy dense limit and compare with numerical ones obtained from a complex Langevin evolution. Furthermore we make use of indirect indicators to check for incorrect convergence of the underlying complex Langevin evolution. The method allows the numerical evaluation of observables at arbitrary values of the chemical potential. We evaluate the results and compare to the (0 + 1)-dimensional case.

Complex Langevin dynamics for chiral random matrix theory

“…The success and failure, observed as a function of the quark mass in the Langevin simulation of chiral random matrix theory, is quite similar to that observed in the 0+1 dimensional Thirring model [19]. Langevin simulations of the Thirring model have not been performed as a part of this work, but it is natural to expect that the same mechanism is responsible for the incorrect dynamics observed in [19].…”

“…Langevin simulations of the Thirring model have not been performed as a part of this work, but it is natural to expect that the same mechanism is responsible for the incorrect dynamics observed in [19].…”

“…We use this to predict regions of successful and failed convergence in two previously studied U (1) models [11,18]. It is likely also to explain the crossover from successful to failed complex Langevin dynamics in other models with a logarithm in the action such as the Thirring model [19].…”

Monte Carlo algorithm for simulating fermions on Lefschetz thimbles

“…This model su↵ers from sign problem and have been used as a toy model for testing ideas such as complex Langevin dynamics [7,35,36] and hybrid Monte Carlo on Lefschetz thimbles [20,21]. The model is fermionic system with a quartic interaction and has the following continuum Euclidean Lagrangian…”

“…For real values of µ, the determinant is complex and the model has a sign problem. The lattice formulation of this model with staggered fermions has the partition function [7,35,36]…”