Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas

TL;DR

This paper introduces a configuration-interaction Monte Carlo method that effectively estimates the ground-state energy of fermionic systems, overcoming the sign problem by using a guiding wave function, demonstrated on a trapped unitary Fermi gas.

Contribution

The paper presents a novel Monte Carlo approach utilizing antisymmetric geminal product wave functions to address the fermionic sign problem in shell model calculations.

Findings

Accurately estimates ground-state energies for trapped unitary Fermi gases.

Provides upper bounds on energies that compare well with exact and previous Monte Carlo results.

Demonstrates effectiveness of guiding wave functions in reducing the sign problem.

Abstract

We develop a quantum Monte Carlo method to estimate the ground-state energy of a fermionic many-particle system in the configuration-interaction shell model approach. The fermionic sign problem is circumvented by using a guiding wave function in Fock space. The method provides an upper bound on the ground-state energy whose tightness depends on the choice of the guiding wave function. We argue that the antisymmetric geminal product class of wave functions is a good choice for guiding wave functions. We demonstrate our method for the trapped two-species fermionic cold atom system in the unitary regime of infinite scattering length using the particle-number projected Hartree-Fock-Bogoliubov wave function as the guiding wave function. We estimate the ground-state energy and energy-staggering pairing gap as a function of the number of particles. Our results compare favorably with exact numerical diagonalization results and with previous coordinate-space Monte Carlo calculations.