Optimized Broad-Histogram Ensembles for the Simulation of Quantum Systems

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.

15 pages, 13 figures

References in corpus (7)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The ALPS project release 1.3: open source software for strongly correlated systems
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids
• Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles