Stochastic Series Expansion Methods

TL;DR

The paper reviews the Stochastic Series Expansion (SSE) quantum Monte Carlo method, highlighting its efficiency, extensions, sampling schemes, estimators, and applications in simulating quantum spin and boson systems.

Contribution

It provides a comprehensive overview of the SSE method, including recent developments, extensions, and practical applications in quantum Monte Carlo simulations.

Findings

SSE is efficient for quantum spin and boson models.

Extensions to ground state projection and quantum annealing are discussed.

Sampling schemes like loop and cluster updates improve simulation efficiency.

Abstract

The Stochastic Series Expansion (SSE) technique is a quantum Monte Carlo method that is especially efficient for many quantum spin systems and boson models. It was the first generic method free from the discretization errors affecting previous path integral based approaches. These lecture notes give a brief overview of the SSE method and its applications. In the introductory section, the representation of quantum statistical mechanics by the power series expansion of ${\rm e}^{-\beta H}$ will be compared with path integrals in discrete and continuous imaginary time. Extensions of the SSE approach to ground state projection and quantum annealing in imaginary time will also be briefly discussed. The later sections introduce efficient sampling schemes (loop and cluster updates) that have been developed for many classes of models. A summary of generic forms of estimators for important observables are also given. Applications are discussed in the last section.