Recent progress on cluster and meron algorithms for strongly correlated systems

TL;DR

This paper reviews recent advances in cluster and meron algorithms that improve Monte Carlo simulations of strongly correlated quantum systems, addressing challenges like the sign problem and extending to gauge theories.

Contribution

It outlines the construction of cluster and meron algorithms, illustrating their application to fermionic systems, gauge theories, and solutions to the sign problem.

Findings

Cluster algorithms enhance simulation efficiency for strongly correlated systems.

Meron algorithms can mitigate the sign problem in specific cases.

Extensions to Abelian gauge theories are discussed.

Abstract

Ab-initio studies of strongly interacting bosonic and fermionic systems is greatly facilitated by efficient Monte Carlo algorithms. This article emphasizes this requirement, and outlines the ideas behind the construction of the cluster algorithms and illustrates them via specific examples. Numerical studies of fermionic systems at finite densities and at real-times are sometimes hindered by the infamous sign problem, which is also discussed. The construction of meron cluster algorithms, which can solve certain sign problems are discussed. Cluster algorithms which can simulate certain pure Abelian gauge theories (realized as quantum link models) are also discussed.