对数正态Rosenzweig-Porter模型中的脆弱扩展相

Ivan M Khaymovich, V. Kravtsov, B. Altshuler, L. Ioffe
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引用次数: 35

摘要

本文提出了Rosenzweig-Porter (RP)模型的一个扩展,即LN-RP模型,其中非对角矩阵元素具有宽的对数正态分布。我们认为该模型更适合于描述一般的多体定位问题。与RP模型相反,在LN-RP模型中出现了一个新的弱遍历相,其特征是完全遍历相遵循的基-旋转破缺对称性。因此,LN-RP模型中除了局部化和遍历过渡之外,还存在两个遍历相之间的过渡(FWE过渡)。我们提出了新的非遍历相稳定性判据,给出了局部化和遍历过渡的点,并证明了LN-RP模型中的Anderson局部化过渡是不连续的,而不是传统RP模型中的。我们还建立了FWE转换的判据,并得到了模型的全相图。我们发现对数正态尾的截断缩小了弱遍历相的区域,恢复了多重分形和完全遍历相。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fragile extended phases in the log-normal Rosenzweig-Porter model
In this paper we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We argue that this model is more suitable to describe a generic many body localization problem. In contrast to RP model, in LN-RP model a new, weakly ergodic phase appears that is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Therefore, in addition to the localization and ergodic transitions in LN-RP model there exists also the transition between the two ergodic phases (FWE transition). We suggest new criteria of stability of the non-ergodic phases which give the points of localization and ergodic transitions and prove that the Anderson localization transition in LN-RP model is discontinuous, in contrast to that in a conventional RP model. We also formulate the criterion of FWE transition and obtain the full phase diagram of the model. We show that truncation of the log-normal tail shrinks the region of weakly-ergodic phase and restores the multifractal and the fully-ergodic phases.
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