Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model

TL;DR

This paper investigates how anisotropy in the Hubbard model affects magnetic correlations and thermodynamics during the 2D-3D crossover, revealing potential for enhanced antiferromagnetic order and a cooling protocol via dimensionality change.

Contribution

It numerically analyzes the 2D-3D crossover in the Hubbard model with anisotropic tunneling, highlighting effects on magnetic structure and entropy, and proposes a novel cooling method.

Findings

Anisotropy can enhance magnetic structure factor below optimal interaction strength.

Maximum structure factor does not surpass isotropic 3D at optimal U/t.

Entropy increases as the system transitions from 3D to 2D, enabling adiabatic cooling.

Abstract

The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using Determinant Quantum Monte Carlo, a simple realization of anisotropy in the 3D Hubbard model in which the tunneling between planes, $t_\perp$, is unequal to the intraplane tunneling $t$. This model interpolates between the three-dimensional isotropic ($t_\perp = t$) and two-dimensional ($t_\perp =0$) systems. We show that at fixed interaction strength to tunneling ratio ($U/t$), anisotropy can enhance the magnetic structure factor relative to both 2D and 3D results. However, this enhancement occurs at interaction strengths below those for which the N\'eel temperature $T_{\rm N\acute{e}el}$ is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal $U/t$. We characterize the 2D-3D crossover in terms of the magnetic structure factor, real space spin correlations, number of doubly-occupied sites, and thermodynamic observables. An interesting implication of our results stems from the entropy's dependence on anisotropy. As the system evolves from 3D to 2D, the entropy at a fixed temperature increases. Correspondingly, at fixed entropy, the temperature will decrease going from 3D to 2D. This suggests a cooling protocol in which the dimensionality is adiabatically changed from 3D to 2D.