Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model

Journal Article · Tue Sep 29 00:00:00 EDT 2020 · Physical Review A

DOI:https://doi.org/10.1103/physreva.102.033340· OSTI ID:1802698

Ibarra-García-Padilla, Eduardo ^[1]; Mukherjee, Rick ^[2]; Hulet, Randall G. ^[3]; Hazzard, Kaden R. A. ^[3]; Paiva, Thereza ^[4]; Scalettar, Richard T. ^[5]

---

1. Rice Univ., Houston, TX (United States); OSTI
2. Imperial College, London (United Kingdom)
3. Rice Univ., Houston, TX (United States)
4. Universidade Federal do Rio de Janeiro (Brazil)
5. Univ. of California, Davis, CA (United States)

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 the determinant quantum Monte Carlo method, a simple realization of anisotropy in the three-dimensional (3D) Hubbard model in which the tunneling between planes, $$t_⊥$$, is unequal to the intraplane tunneling $$\textit{t}$$. This model interpolates between the three-dimensional isotropic ($$t_⊥ = t$$) and two-dimensional (2D;$$t_⊥$$ = 0) systems. In this work, we show that at fixed interaction strength to tunneling ratio ($$\textit{U/t}$$), 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 Néel temperature $$T_{\text{Néel}}$$ is largest, in such a way that the structure factor cannot be made to exceed its value in isotropic 3D systems at the optimal $$\textit{U/t}$$. 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.

• Research Organization: Univ. of California, Davis, CA (United States)
• Sponsoring Organization: Engineering and Physical Sciences Research Council (EPSRC); European Unions Horizon 2020 Programme; National Science Foundation (NSF); US Army Research Office (ARO); US Department of the Navy, Office of Naval Research (ONR); USDOE Office of Science (SC); Welch Foundation
• Grant/Contract Number: SC0014671
• OSTI ID: 1802698
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 3 Vol. 102; ISSN 2469-9926
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
Optics
Physics