Roy Sthitadhi, Logan David E
Physical and Theoretical Chemistry, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom.
Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom.
Phys Rev Lett. 2020 Dec 18;125(25):250402. doi: 10.1103/PhysRevLett.125.250402.
Many-body localization in interacting quantum systems can be cast as a disordered hopping problem on the underlying Fock-space graph. A crucial feature of the effective Fock-space disorder is that the Fock-space site energies are strongly correlated-maximally so for sites separated by a finite distance on the graph. Motivated by this, and to understand the effect of such correlations more fundamentally, we study Anderson localization on Cayley trees and random regular graphs, with maximally correlated disorder. Since such correlations suppress short distance fluctuations in the disorder potential, one might naively suppose they disfavor localization. We find however that there exists an Anderson transition, and indeed that localization is more robust in the sense that the critical disorder scales with graph connectivity K as sqrt[K], in marked contrast to KlnK in the uncorrelated case. This scaling is argued to be intimately connected to the stability of many-body localization. Our analysis centers on an exact recursive formulation for the local propagators as well as a self-consistent mean-field theory; with results corroborated using exact diagonalization.
相互作用量子系统中的多体局域化可归结为基础福克空间图上的无序跳跃问题。有效福克空间无序的一个关键特征是，福克空间格点能量具有强相关性——在图上被有限距离隔开的格点之间相关性最强。受此启发，并为了更深入地理解这种相关性的影响，我们研究了具有最大相关无序的凯莱树和随机正则图上的安德森局域化。由于这种相关性抑制了无序势中的短距离涨落，人们可能天真地认为它们不利于局域化。然而，我们发现存在安德森转变，并且实际上局域化更稳健，因为临界无序随图的连通性K按√K缩放，这与不相关情况下的KlnK形成鲜明对比。这种缩放被认为与多体局域化的稳定性密切相关。我们的分析集中在局部传播子的精确递归公式以及自洽平均场理论上；通过精确对角化验证了结果。
