Canonical and Grand Canonical Ensemble Expectation Values from Quantum Monte Carlo Simulations

TL;DR

This paper presents a method to derive canonical ensemble expectation values from grand canonical quantum Monte Carlo simulations, enabling analysis across all particle sectors with multiple simulations at different chemical potentials, demonstrated on the 2D Hubbard model.

Contribution

It introduces a technique to extract canonical ensemble results from grand canonical quantum Monte Carlo data, broadening the applicability of such simulations.

Findings

Method successfully applied to the 2D Hubbard model

Allows continuous extraction of grand canonical expectation values

Requires only a modest number of simulations at different chemical potentials

Abstract

We show how canonical ensemble expectation values can be extracted from quantum Monte Carlo simulations in the grand canonical ensemble. In order to obtain results for all particle sectors, a modest number of grand canonical simulations must be performed, each at a different chemical potential. From the canonical ensemble results, grand canonical expectation values can be extracted as a continuous function of the chemical potential. Results are presented from the application of this method to the two-dimensional Hubbard model.