Universal probes for antiferromagnetic correlations and entropy in cold fermions on optical lattices

TL;DR

This paper identifies universal signatures of antiferromagnetic correlations and entropy in cold fermionic atoms on optical lattices, providing insights into the crossover from charge to spin regimes relevant for experiments.

Contribution

It introduces universal probes based on double occupancy and NNN spin correlations to detect antiferromagnetic physics in cold atom systems.

Findings

Double occupancy minimum at entropy s* = ln(2) signals AF crossover.

Linear increase of NNN spin correlations for s < s*.

Long-range AF order detectable via NNN correlations.

Abstract

We determine antiferromagnetic (AF) signatures in the half-filled Hubbard model at strong coupling on a cubic lattice and in lower dimensions. Upon cooling, the transition from the charge-excitation regime to the AF Heisenberg regime is signaled by a universal minimum of the double occupancy at entropy s=S/(N k_B)=s*=ln(2) per particle and a linear increase of the next-nearest neighbor (NNN) spin correlation function for s<s*. This crossover, driven by a gain in kinetic exchange energy, appears as the essential AF physics relevant for current cold-atom experiments. The onset of long-range AF order (at low s on cubic lattices) is hardly visible in nearest-neighbor spin correlations versus s, but could be detected in spin correlations at or beyond NNN distances.