Niermann Tristan, Hoppe Hannes, Manthe Uwe
Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany.
J Chem Phys. 2024 Oct 7;161(13). doi: 10.1063/5.0228399.
The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is an efficient method to study quantum dynamics in real and imaginary time. The present work explores its potential to describe quantum fluids. The multi-layer MCTDH approach in second quantization representation is used to study lattice models beyond one dimension at finite temperatures. A scheme to map the lattice sites onto the MCTDH tree representation for multi-dimensional lattice models is proposed. A statistical sampling scheme previously used in MCTDH calculations is adapted to facilitate an efficient description of the thermal ensemble. As example, a two-dimensional hard-core Bose-Hubbard model is studied considering up to 64 × 64 lattice sites. The single particle function basis set size required to obtain converged results is found to not increase with the lattice size. The numerical results properly simulate the finite temperature Berezinskii-Kosterlitz-Thouless phase transition.
多层多组态含时 Hartree（MCTDH）方法是研究实时间和虚时间量子动力学的一种有效方法。本工作探索了其描述量子流体的潜力。采用二次量子化表示中的多层 MCTDH 方法来研究有限温度下的一维以上晶格模型。提出了一种将晶格位点映射到多维晶格模型的 MCTDH 树表示的方案。对先前在 MCTDH 计算中使用的统计抽样方案进行了调整，以利于对热系综进行有效描述。作为示例，研究了一个二维硬核玻色 - 哈伯德模型，考虑了多达 64×64 的晶格位点。发现获得收敛结果所需的单粒子函数基组大小不随晶格大小增加。数值结果正确地模拟了有限温度下的 Berezinskii - Kosterlitz - Thouless 相变。
