Efficient simulation of relativistic fermions via vertex models

TL;DR

This paper introduces an efficient algorithm for simulating strongly interacting relativistic fermions in two-dimensional field theories by mapping them to vertex models, overcoming critical slowing down and enabling massless limit simulations.

Contribution

It presents a novel simulation algorithm that maps fermionic dynamics to vertex models, allowing efficient, direct simulations in the massless limit across arbitrary dimensions.

Findings

Successfully applied to the Gross-Neveu model

Effective in the strong coupling limit of the Schwinger model

Eliminates critical slowing down in simulations

Abstract

We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped to statistical vertex models and our proposal is in fact an efficient simulation algorithm for generic vertex models in arbitrary dimensions. The algorithm essentially eliminates critical slowing down by sampling two-point correlation functions and it allows simulations directly in the massless limit. Moreover, it generates loop configurations with fluctuating topological boundary conditions enabling to simulate fermions with arbitrary periodic or anti-periodic boundary conditions. As illustrative examples, the algorithm is applied to the Gross-Neveu model and to the Schwinger model in the strong coupling limit.