Vertex Models and Quantum Spin Systems: a nonlocal approach

TL;DR

This paper introduces a nonlocal loop-algorithm within a cluster framework that effectively reduces critical slowing down in vertex models and quantum spin systems, demonstrated through numerical results on the 6-vertex and F-models.

Contribution

It presents a novel loop-algorithm that improves simulation efficiency for vertex models and quantum spin systems, including modifications for complex cases.

Findings

Loop-algorithm reduces critical slowing down.

Numerical results show effectiveness for the 6-vertex and F-models.

Algorithm adaptable to complex quantum spin systems.

Abstract

Within a general cluster framework, we discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail. For the F-model, we present numerical results that demonstrate the effectiveness of the loop algorithm. We discuss how to modify the original algorithm for some more complicated situations, especially for quantum spin systems in one and two dimensions.