An efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations

TL;DR

This paper presents a new, efficient grand-canonical twist averaging method for quantum Monte Carlo calculations that reduces sampling errors and improves ground state energy estimates, even with few twists.

Contribution

The paper introduces a novel grand-canonical twist averaging technique that evaluates the grand potential, enhancing accuracy over traditional methods in quantum Monte Carlo simulations.

Findings

Reduces sampling errors in twist-dependent fluctuations

Produces more accurate ground state energies with fewer twists

Applicable to various materials like electron gas and metals

Abstract

We introduce a simple but efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations. By evaluating the thermodynamic grand potential instead of the ground state total energy, we greatly reduce the sampling errors caused by twist-dependent fluctuations in the particle number. We apply this method to the electron gas and to metallic lithium, aluminum, and solid atomic hydrogen. We show that, even when using a small number of twists, grand-canonical twist averaging of the grand potential produces better estimates of ground state energies than the widely used canonical twist-averaging approach.