Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions

TL;DR

This paper introduces a sign-free stochastic mean-field quantum Monte Carlo method for studying strongly correlated ultracold fermions, avoiding the sign problem and enabling accurate ground state calculations.

Contribution

A novel projector quantum Monte Carlo approach that reconstructs many-body states from evolving Slater determinants without encountering the sign problem.

Findings

Accurate ground-state energies for the 2D Hubbard model

Correlation functions computed successfully

Validation with unitary Fermi gas simulations

Abstract

We propose a new projector quantum Monte-Carlo method to investigate the ground state of ultracold fermionic atoms modeled by a lattice Hamiltonian with on-site interaction. The many-body state is reconstructed from Slater determinants that randomly evolve in imaginary-time according to a stochastic mean-field motion. The dynamics prohibits the crossing of the exact nodal surface and no sign problem occurs in the Monte-Carlo estimate of observables. The method is applied to calculate ground-state energies and correlation functions of the repulsive two-dimensional Hubbard model. Numerical results for the unitary Fermi gas validate simulations with nodal constraints.