Double occupancy as a universal probe for antiferromagnetic correlations and entropy in cold fermions on optical lattices

TL;DR

This paper demonstrates that double occupancy measurements serve as a universal indicator of antiferromagnetic correlations and entropy levels in cold fermionic systems across different dimensions, providing guidance for experimental detection.

Contribution

It provides a comprehensive analysis of double occupancy as a probe for AF correlations across 1D, 2D, and 3D systems, highlighting its near universality and experimental relevance.

Findings

Double occupancy correlates with AF correlations across dimensions.

D(s) approaches log(2) at strong coupling, indicating entropy thresholds.

Long-range order is less relevant for current AF detection in cold fermions.

Abstract

We verify signatures of antiferromagnetic (AF) correlations in the double occupancy D [Gorelik et al., PRL 105, 065301 (2010)] and study their dimensional dependence using direct quantum Monte Carlo in dimensions d=2,3 and Bethe Ansatz in d=1. We find quantitative agreement with dynamical mean-field theory (DMFT) in the cubic case and qualitative agreement down to d=1. As a function of entropy s=S/(N k_B), D is nearly universal with respect to d; the minimum in D(s) approaches s=log(2) at strong coupling, as predicted by DMFT. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve s<log(2)/2 and should consider lower dimensions, for which the AF effects are larger.