论文标题
（多）分形特征态对哈密顿扰动的敏感性
Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian
论文作者
论文摘要
我们研究了由从高斯Rosenzweig-porter随机矩阵集合合奏中绘制的hamiltonian控制的孤立量子系统对受小参数控制的扰动的响应。我们专注于状态的密度，状态的局部密度以及特征功能振幅重叠相关函数，这些函数使用映射到超对称非线性非线性Sigma模型进行了精确计算。我们表明，本征性忠诚度对扰动参数的敏感性可以用这些相关函数表示，并且在定位过渡时峰值高峰：它独立于颈中的有效障碍强度，在局部相位逐渐降低定位期的障碍呈成倍增长。作为基质大小的函数，富达度的易感性在沿阵行相中保持恒定，并且在适度强的疾病下的分形和局部阶段增加。我们表明，绝缘阶段内部存在关键的疾病强度，因此，对于比临界更强的疾病，保真度易感性随着系统规模的增加而降低。在Sels和Polkovnikov [Phys。 Rev. E 104，054105（2021）]用于无序XXZ自旋链中的归一化富度敏感性。
We study the response of an isolated quantum system governed by the Hamiltonian drawn from the Gaussian Rosenzweig-Porter random matrix ensemble to a perturbation controlled by a small parameter. We focus on the density of states, local density of states and the eigenfunction amplitude overlap correlation functions which are calculated exactly using the mapping to the supersymmetric nonlinear sigma model. We show that the susceptibility of eigenfunction fidelity to the parameter of perturbation can be expressed in terms of these correlation functions and is strongly peaked at the localization transition: It is independent of the effective disorder strength in the ergodic phase, grows exponentially with increasing disorder in the fractal phase and decreases exponentially in the localized phase. As a function of the matrix size, the fidelity susceptibility remains constant in the ergodic phase and increases in the fractal and in the localized phases at modestly strong disorder. We show that there is a critical disorder strength inside the insulating phase such that for disorder stronger than the critical the fidelity susceptibility decreases with increasing the system size. The overall behavior is very similar to the one observed numerically in a recent work by Sels and Polkovnikov [Phys. Rev. E 104, 054105 (2021)] for the normalized fidelity susceptibility in a disordered XXZ spin chain.
