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

O Juillet

doi:10.1088/1367-2630/9/6/163

Abstract

We propose a new projector quantum Monte-Carlo method to investigate the ground state of ultracold fermionic atoms modelled 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.

Highlights

Since the experimental achievement of Fermi degeneracy [1] with an atomic vapor, a considerable attention has been attracted by the physics of dilute ultracold fermions
The ability to tune many parameters, such as temperature, density or inter-particle interactions, makes atomic Fermi gases ideal candidates to understand a wealth of phenomena relevant for physical systems ranging from nuclear matter to high-temperature superconductors
Using several standing laser beams, ultracold atoms can be loaded in optical lattices where they experience all the strong many-body correlations described by the Hubbard model of solid-state physics [8,9]

Summary

Introduction

Since the experimental achievement of Fermi degeneracy [1] with an atomic vapor, a considerable attention has been attracted by the physics of dilute ultracold fermions. We investigate a new Monte-Carlo scheme to study strongly correlated ground states of ultracold fermions interacting on a lattice. The projection onto the ground state is performed through a reformulation of the imaginary-time Schrödinger equation in terms of Slater determinants undergoing a Brownian motion driven by the Hartree-Fock Hamiltonian. Such exact stochastic extensions of the mean-field approaches have been recently proposed for boson systems [14,15]. For a system of fermions interacting through a binary potential, we first introduce a set of hermitian one-body operators As (s = 0,1,L) allowing to rewrite the model Hamiltonian Has a quadratic form:.

If the two Slater determinants ψ

Findings

Conclusion