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 sites) and very long times (up to ). We find that, in the 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 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 grows as for the decay governed by rare regions. At longest times and moderately strong disorder, approaches the limiting value 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 , 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 网站)和很长的时间(最多 )。我们发现,在在极限情况下,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: 成长为 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, 接近极限值 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,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。