Cluster Algorithm for Vertex Models

TL;DR

This paper introduces a loop cluster algorithm that significantly reduces critical slowing down in vertex model simulations, applicable to various models including the F model and quantum spin systems.

Contribution

The paper presents a novel loop cluster algorithm that improves simulation efficiency for vertex models and related quantum systems.

Findings

Reduces critical slowing down in vertex model simulations

Applicable to F model and other vertex models

Effective for quantum spin system simulations

Abstract

We present a new type of cluster algorithm that strongly reduces critical slowing down in simulations of vertex models. Since the clusters are closed paths of bonds, we call it the {\em loop algorithm}. The basic steps in constructing a cluster are the break-up and the freezing of vertices. We concentrate on the case of the F model, which is a subset of the 6-vertex model exhibiting a Kosterlitz-Thouless transition. The loop algorithm is also applicable to simulations of other vertex models and of one and two-dimensional quantum spin systems.