The Loop-Cluster Algorithm for the Case of the 6 Vertex Model

TL;DR

This paper introduces a generalized loop-cluster algorithm for the 6 vertex model, extending previous work on the F model, and discusses its application to quantum spin system simulations.

Contribution

The paper develops a generalized loop algorithm for the 6 vertex model, incorporating the principle of least freezing for parameter selection.

Findings

Algorithm successfully applied to the 6 vertex model

Provides a framework for simulating quantum spin systems

Guides parameter choice for efficient simulations

Abstract

We present the loop algorithm, a new type of cluster algorithm that we recently introduced for the F model. Using the framework of Kandel and Domany, we show how to GENERALIZE the algorithm to the arrow flip symmetric 6 vertex model. We propose the principle of least possible freezing as the guide to choosing the values of free parameters in the algorithm. Finally, we briefly discuss the application of our algorithm to simulations of quantum spin systems. In particular, all necessary information is provided for the simulation of spin $\half$ Heisenberg and $xxz$ models.