We apply the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) to systems of bosons or fermions in lattices described by Hubbard type Hamiltonians with long-range or short-range interparticle interactions. The wavefunction is expanded in a variationally optimized time-dependent many-body basis generated by a set of effective creation operators that are related to the original particle creation operators by a time-dependent unitary transform. We use the time-dependent variational principle for the coefficients of this transform as well as the expansion coefficients of the wavefunction in the time-dependent many-body basis as variational parameters to derive equations of motion. The convergence of MCTDH-X is shown by comparing its results to the exact diagonalization of one-, two-, and three-dimensional lattices filled with bosons with contact interactions. We use MCTDH-X to study the buildup of correlations in the long-time splitting dynamics of a Bose-Einstein condensate loaded into a large two-dimensional lattice subject to a barrier that is ramped up in the center. We find that the system is split into two parts with emergent time-dependent correlations that depend on the ramping time -- for most barrier-raising-times the system becomes two-fold fragmented, but for some of the very fast ramps, the system shows revivals of coherence.
The multiconfigurational time-dependent Hartree method for bosons with internal degrees of freedom: Theory and composite fragmentation of multi-component Bose-Einstein condensates
Negative Interaction Quench Dynamics of Density-Ordered Dipolar Bosons in a One-Dimensional Optical Lattice
University of Haifa（海法大学）；The Maharaja Sayajirao University of Baroda（巴罗达马哈拉贾·萨亚吉拉奥大学）；Universidade Federal de Pernambuco（伯南布哥联邦大学）；Universidade de São Paulo（圣保罗大学）
Dynamical localization of interacting ultracold atoms in one-dimensional quasi-periodic potentials
Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；Department of Biomedical Engineering, Texas A&M University（德州农工大学生物医学工程系）；Department of Physics, Presidency University（总统大学物理系）
Entropy Signatures of Collective Modes and Vortex Dynamics in Rotating Two--Dimensional Bose--Einstein Condensates
Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；School of Mathematics, Statistics and Physics, Newcastle University（纽卡斯尔大学数学、统计与物理学院）；Department of Physics, Asansol Girls’ College（阿桑索尔女子学院物理系）；Instituto de Física, Universidade de São Paulo（圣保罗大学物理研究所）；Departamento de Química, Universidad Autónoma Metropolitana - Iztapalapa（墨西哥自治大学伊兹塔帕拉帕化学系）
