Quantum Monte Carlo simulations of antiferromagnetism in ultracold fermions on optical lattices within real-space dynamical mean-field theory

TL;DR

This paper develops a parallel quantum Monte Carlo implementation of real-space dynamical mean-field theory to study antiferromagnetism in ultracold fermions on optical lattices, revealing temperature effects and limitations of local density approximation.

Contribution

It introduces a scalable quantum Monte Carlo method for inhomogeneous fermionic systems and applies it to analyze magnetic order in cold-atom experiments.

Findings

Signatures of the Néel transition identified in observable quantities.

Local density approximation fails for ordered phases.

A 'slab' approximation enables large system simulations with minimal accuracy loss.

Abstract

We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary mixture of repulsively interacting fermionic atoms harmonically trapped in an optical lattice. We explore temperature effects and establish signatures of the N\'{e}el transition in observables directly accessible in cold-atom experiments; entropy estimates are also provided. We demonstrate that the local density approximation (LDA) fails for ordered phases. In contrast, a "slab" approximation allows us to reach experimental system sizes with O(10^5) atoms without significant loss of accuracy.