Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model
Thermodynamics and magnetism in the two-dimensional to three-dimensional crossover of the Hubbard model
复制标题
DOI：
10.1103/physreva.102.033340
复制
发表时间：
2020-09
影响因子：
2.9
通讯作者：
E. Ibarra-García-Padilla;R. Mukherjee;R. Hulet;K. Hazzard;T. Paiva;R. Scalettar
中科院分区：
文献类型：
--
作者：
E. Ibarra-García-Padilla;R. Mukherjee;R. Hulet;K. Hazzard;T. Paiva;R. Scalettar
在光学晶格中实现超冷费米子原子的反铁磁关联是一个重要的成就。实验已经进行了一维，二维和三维，也研究了各向异性配置与较强的隧道在一些晶格方向。这种各向异性与铜氧化物超导体和其他强相关材料的物理学有关。此外，这种各向异性可能被利用来增强AF阶。在这里，我们调查一个简单的实现各向异性的3D哈伯德模型中，平面之间的隧道，$t_\perp$，是不平等的面内隧道$t$。该模型在三维各向同性（$t_\perp = t$）和二维（$t_\perp =0$）系统之间插值。我们发现，在固定的相互作用强度隧穿比（$U/t$），各向异性可以提高相对于2D和3D结果的磁结构因子。然而，这种增强发生在相互作用强度低于那些尼尔温度$T_{\rm N\acute{e}el}$是最大的，在这样一种方式，结构因子不能超过其值在各向同性的三维系统在最佳的$U/t$。我们用磁结构因子、真实的空间自旋关联、双占据位点数和热力学观测量来表征2D-3D交叉。我们的结果的一个有趣的含义源于熵的各向异性的依赖。随着系统从3D发展到2D，在固定温度下的熵增加。相应地，在固定熵下，温度将从3D降低到2D。这表明了一种冷却协议，其中维度从3D动态地改变为2D。
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 investigate 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 Neel 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.