论文标题
在对数正常的rosenzweig-porter模型中脆弱的千古相
Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
论文作者
论文摘要
在本文中，我们建议Rosenzweig-Porter（RP）模型的LN-RP模型的扩展，其中Off-Diagonal矩阵元素具有较宽的对数正态分布。我们认为该模型更适合描述一个通用的许多身体定位问题。与RP模型相反，在LN-RP模型中，出现了一个脆弱的弱颈阶段，其特征是基于基础的反旋转对称性，该相位相位阶段（也存在于该模型中）在热力学极限中严格尊重。因此，除了在LN-RP模型中的定位和厄乳转变外，还存在两个千古相（FWE跃迁）之间的跃迁。我们建议非癌相位的稳定性新标准，这些标准给出了定位点和偏僻的过渡点，并证明了LN-RP模型中的Anderson定位过渡涉及特征功能支持集的分形维度的跳跃。我们还制定了FWE过渡的标准，并获得模型的完整相图。我们表明，对数正态尾部的截断会缩小弱连电相的区域，并恢复多重分子和完全连接的相位。
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 fragile weakly ergodic phase appears that is characterized by broken basis-rotation symmetry which the fully-ergodic phase, also present in this model, strictly respects in the thermodynamic limit. 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 involves a jump in the fractal dimension of the eigenfunction support set. 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.
