Blockspin Cluster Algorithms for Quantum Spin Systems

TL;DR

This paper introduces blockspin cluster algorithms for quantum spin systems, improving simulation efficiency by collective cluster updates and addressing slowing down issues present in standard methods.

Contribution

The paper develops novel blockspin cluster algorithms for quantum spin systems, mapping them to classical models and enhancing simulation efficiency.

Findings

Algorithms effectively reduce slowing down in simulations

Cluster updates improve computational efficiency

Method applicable to 1D and higher-dimensional systems

Abstract

Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are maped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the problems of slowing down from which standard algorithms are suffering.