Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d staggered fermion model

TL;DR

This paper employs the Meron-Cluster algorithm to numerically investigate a (2+1)-dimensional staggered fermion model with four-fermion interactions, revealing spontaneous chiral symmetry breaking and a 2D Ising universality class phase transition.

Contribution

It demonstrates the effectiveness of the Meron-Cluster algorithm in studying a challenging fermion model inaccessible to standard methods, providing high-precision results.

Findings

Chiral symmetry is spontaneously broken at low temperatures.

The finite-temperature phase transition belongs to the 2D Ising universality class.

The model's behavior aligns with theoretical expectations for such fermionic systems.

Abstract

The recently developed Meron-Cluster algorithm completely solves the exponentially difficult sign problem for a number of models previously inaccessible to numerical simulation. We use this algorithm in a high-precision study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a four-fermion interaction. This model cannot be explored using standard algorithms. We find that the Z(2) chiral symmetry of this model is spontaneously broken at low temperatures and that the finite-temperature chiral phase transition is in the universality class of the 2-d Ising model, as expected.