Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems

TL;DR

This paper introduces a new quantum Monte Carlo algorithm based on a framework by Syljuasen and Sandvik, extending the conventional loop algorithm for quantum spin systems, and provides detailed parameters for the XXZ model.

Contribution

It presents a natural extension of the loop algorithm within the Syljuasen and Sandvik framework, including a comprehensive table of parameters for the XXZ model.

Findings

Developed an efficient algorithm for quantum spin systems

Provided a complete table of vertex densities and scattering probabilities

Enhanced the applicability of loop algorithms to general XXZ models

Abstract

Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.