We present a study of thermalisation of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalises with the rest of the system as its environment. We explore numerically the existence of thermalisation over a range of system parameters, such as the interaction strength, system size and the strength of the coupling between the subsystem and the rest of the lattice. We find thermalisation over a wide range of parameters and that interactions are crucial for efficient thermalisation of small systems. We relate this thermalisation behaviour to the eigenstate thermalisation hypothesis and quantify numerically the extent to which eigenstate thermalisation holds. We also verify our numerical results theoretically with the help of previously established results from random matrix theory for the local density of states, particularly the finite-size scaling for the onset of thermalisation.
Thermodynamics of the three-dimensional Hubbard model: Implications for cooling cold atomic gases in optical lattices
本文对三维费米子哈伯德模型的热力学性质进行了全面的研究，并将其应用于受光晶格和囚禁势约束的冷费米子原子。我们的研究集中在当前实验感兴趣的温度范围内。我们采用两种理论方法-动态平均场论和高温系列-和执行比较基准，以界定各自的有效性范围。特别注意的是，致力于了解这个系统的热力学性质对冷却的影响。考虑到非均匀晶格中的局域占位分布函数，我们证明了，在绝热演化下，任何可观测的变化（例如，温度）可以方便地分解成两个不同的贡献。第一个贡献是由于演化过程中陷阱中原子的重新分布，而第二个贡献来自于可观测的内在变化。最后，我们提供了J. - S. Bernier等人，Phys. Rev. A 79，061601（2009）通过将该方法应用于理想化模型来计算。
From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）；Collège de France（法兰西学院）；CNRS（法国国家科学研究中心）；ENS-Université PSL（巴黎高等师范学院-巴黎文理研究大学）；Sorbonne Université（索邦大学）
