Cluster simulation of relativistic fermions in two space-time dimensions

TL;DR

This paper develops an exact dimer and loop representation for Majorana-Wilson lattice fermions in two dimensions, enabling an efficient cluster algorithm with improved estimators and new observables for Monte Carlo simulations.

Contribution

It introduces a novel exact dimer and loop representation for 2D lattice fermions, leading to a highly efficient cluster algorithm compatible with gauge interactions.

Findings

Successful numerical demonstration for critical free fermions

Efficient cluster algorithm with fluctuating boundary conditions

Enhanced observables accessible via the new representation

Abstract

For Majorana-Wilson lattice fermions in two dimensions we derive a dimer representation. This is equivalent to Gattringer's loop representation, but is made exact here on the torus. A subsequent dual mapping leads to yet another representation in which a highly efficient Swendsen-Wang type cluster algorithm is constructed. It includes the possibility of fluctuating boundary conditions. It also allows for improved estimators and makes interesting new observables accessible to Monte Carlo. The algorithm is compatible with the Gross-Neveu as well as an additional Z(2) gauge interaction. In this article numerical demonstrations are reported for critical free fermions.