Anomalous discrete chiral symmetry in the Gross-Neveu model and loop gas simulations

TL;DR

This paper explores the anomalous behavior of discrete chiral symmetry in the Gross-Neveu model, employing loop gas simulations and a novel algorithm to analyze boundary condition effects and phase transitions.

Contribution

It introduces a new approach to account for chiral anomaly in lattice simulations of the Gross-Neveu model using the worm technique.

Findings

Critical line m_c(g) determined for N=6 and N=2.

Demonstrates the impact of boundary conditions on the chiral measure.

Provides a new algorithm incorporating Gross-Neveu interactions in loop gas simulations.

Abstract

We investigate the discrete chiral transformation of a Majorana fermion on a torus. Depending on the boundary conditions the integration measure can change sign. Taking this anomalous behavior into account we define a chiral order parameter as a ratio of partition functions with differing boundary conditions. Then the lattice realization of the Gross-Neveu model with Wilson fermions is simulated using the recent `worm' technique on the loop gas or all-order hopping representation of the fermions. An algorithm is formulated that includes the Gross-Neveu interaction for N fermion species. The critical line m_c(g) is constructed for a range of couplings at N = 6 and for N = 2, the Thirring model, as examples.