Effects of anisotropy in simple lattice geometries on many-body properties of ultracold fermions in optical lattices

TL;DR

This paper explores how anisotropic hopping in optical lattice models affects quantum phase transitions and localization in ultracold fermions, revealing that anisotropy can significantly alter critical temperatures and phase behavior.

Contribution

It provides a detailed analysis of anisotropy effects on the Fermi-Hubbard model using DMFT, highlighting how anisotropy influences phase transitions and localization properties.

Findings

Anisotropy can both suppress and enhance the critical temperature for magnetic transitions.

Density profiles can serve as indicators of anisotropy-driven phase changes.

Localization properties like compressibility are affected by hopping anisotropy.

Abstract

We study the effects of anisotropic hopping amplitudes on quantum phases of ultracold fermions in optical lattices described by the repulsive Fermi-Hubbard model. In particular, using dynamical mean-field theory (DMFT) we investigate the dimensional crossover between the isotropic square and the isotropic cubic lattice. We analyze the phase transition from the antiferromagnetic to the paramagnetic state and observe a significant change in the critical temperature: Depending on the interaction strength, the anisotropy can lead to both a suppression or increase. We also investigate the localization properties of the system, such as the compressibility and double occupancy. Using the local density approximation in combination with DMFT we conclude that density profiles can be used to detect the mentioned anisotropy-driven transitions.