Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems

TL;DR

This paper introduces a feedback algorithm to optimize broad-histogram ensembles in quantum Monte Carlo simulations, significantly improving sampling efficiency by adapting the ensemble based on system behavior, especially near phase transitions.

Contribution

It generalizes a feedback algorithm to optimize sampling distributions in quantum systems within the stochastic series expansion framework, enhancing simulation efficiency.

Findings

Optimized ensembles achieve flat histograms in efficient regimes.

At phase transitions, the algorithm shifts weights to improve sampling.

Enhanced sampling reduces simulation slowdown near critical points.

Abstract

The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback algorithm can be generalized to find optimized sampling distributions for the simulation of quantum systems in the context of the stochastic series expansion (SSE) when defining an extended ensemble in the expansion order. If the chosen update method is efficient, such as non-local updates for systems undergoing a second-order phase transition, the optimized ensemble is characterized by a flat histogram in the expansion order if a variable-length formulation of the SSE is used. Whenever the update method suffers from slowdown, such as at a first-order phase transition, the feedback algorithm shifts weight towards the expansion orders in the transition region, resulting in a non-uniform histogram.