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Dynamics of many-body delocalization in the time-dependent Hartree–Fock approximation
Annals of Physics ( IF 3.0 ) Pub Date : 2021-04-24 , DOI: 10.1016/j.aop.2021.168486
Paul Pöpperl , Elmer V.H. Doggen , Jonas F. Karcher , Alexander D. Mirlin , Konstantin S. Tikhonov

We explore dynamics of disordered and quasi-periodic interacting lattice models using a self-consistent time-dependent Hartree–Fock (TDHF) approximation, accessing both large systems (up to L=400 sites) and very long times (up to t=105). We find that, in the t limit, the many-body localization (MBL) is always destroyed within the TDHF approximation. At the same time, this approximation provides important information on the long-time character of dynamics in the ergodic side of the MBL transition. Specifically, for one-dimensional (1D) disordered chains, we find slow power-law transport up to the longest times, supporting the rare-region (Griffiths) picture. The information on this subdiffusive dynamics is obtained by the analysis of three different observables— temporal decay tβ of real-space and energy-space imbalances as well as domain wall melting—which all yield consistent results. For two-dimensional (2D) systems, the decay is faster than a power law, in consistency with theoretical predictions that β grows as logt for the decay governed by rare regions. At longest times and moderately strong disorder, β approaches the limiting value β=1 corresponding to 2D diffusion. In quasi-periodic (Aubry-André) 1D systems, where rare regions are absent, we find considerably faster decay that reaches the ballistic value β=1, which provides further support to the Griffiths picture of the slow transport in random systems.



中文翻译:

基于时间的Hartree-Fock逼近中的多体离域动力学

我们使用自洽时间相关的Hartree-Fock(TDHF)近似方法,探索无序和准周期相互作用晶格模型的动力学,同时访问两个大型系统(直至 大号=400 网站)和很长的时间(最多 Ť=1个05)。我们发现,在Ť在极限情况下,多体定位(MBL)始终在TDHF逼近范围内被破坏。同时,这种近似提供了有关MBL过渡的遍历一侧动力学的长期特征的重要信息。具体来说,对于一维(1D)无序链,我们发现直到最长时间的幂律传输速度都很慢,这支持了稀有区域(Griffiths)的情况。通过分析三个不同的可观测量(时间衰减)获得有关此亚扩散动力学的信息Ť-β真实空间和能量空间的不平衡以及畴壁融化,这些都会产生一致的结果。对于二维(2D)系统,其衰减比幂定律快,这与理论预测一致:β 成长为 日志Ť对于由稀有地区控制的衰变。在最长的时间和中等强度的疾病中,β 接近极限值 β=1个对应于2D扩散。在缺少稀有区域的准周期(Aubry-André)1D系统中,我们发现衰减更快,达到弹道值β=1个,这为格里菲斯关于随机系统中缓慢传输的图景提供了进一步的支持。

更新日期:2021-04-24
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