Finite-Temperature Auxiliary-Field Quantum Monte Carlo for Bose-Fermi Mixtures

TL;DR

This paper introduces a novel quantum Monte Carlo algorithm that accurately computes finite-temperature properties of Bose-Fermi mixtures, addressing challenges like the sign problem and enabling studies of complex many-body systems.

Contribution

The paper develops the first combined finite-temperature AFQMC method for Bose-Fermi mixtures, improving accuracy and applicability over existing techniques.

Findings

Validated against exact diagonalization for small systems

Compared favorably with mean-field and worm algorithms for larger systems

Discussed methods to control the sign problem in BF-AFQMC

Abstract

We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi Auxiliary-Field Quantum Monte Carlo (BF-AFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in BF-AFQMC. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand BF-AFQMC's reach. The new algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.