发表机构
Institute for Basic Science (IBS); Indian Institute of Technology-Kanpur; Korea University of Science and Technology (UST); Massey University（基础科学研究院; 坎普尔印度理工学院; 韩国科学技术院; 梅西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种定制无序场的方法，使特定能量下的本征态退局域化，局域化长度按$1/|E|^{2/3}$发散，适用于任意维度、跳跃场及厄米与非厄米系统。
AI 中文摘要
我们推导了由特定退局域化波函数的选择细节所定制的无序场。我们首先研究了单向Hatano-Nelson链及其在具有可变权重的$M$-基对角无序下的局域化性质。谱在复平面中形成环，环参数是一个类似于动量的好量子数。所有本征态都是次指数“局域化”的，即波函数绝对值的对数在空间中进行随机游走，并具有相应的长度尺度$\xi_{sel}$，如Silvestrov在1998年对一般Hatano-Nelson链所展示的那样。对于$M=2$且权重相等的实值二元无序，该模型已在《Zeitschrift für Naturforschung A》81 421中求解，得到Cassini卵形谱环，并且在无序强度弱于由跳跃强度设定的临界值时，两个本征态具有发散的次指数局域化长度。当任意$M$和任意权重的无序场被限制在复平面中半径等于跳跃强度的圆上时，圆心将属于谱并属于其中一个谱环，并承载一个具有发散$\xi_{sel}$的类平面波本征态。我们将其推广到为任意晶格维数、任意跳跃场（有序和无序）以及厄米和非厄米系统中给定能量下的给定本征态定制在位无序。我们通过构造一个具有Anderson局域化本征态的一维链来举例说明，该链承载一个具有随机相位的完全退局域化本征态。在接近退局域化态时，局域化长度按$1/|E|^{2/3}$发散。我们的方法可用于系统构造具有任意性质的预定义本征态的无序场。
英文摘要
We derive disorder fields tailored by the details of a choice of a delocalized wave function. We first investigate the unidirectional Hatano-Nelson chain and its localization properties under $M$-base diagonal disorder with variable weights. The spectrum forms loops in the complex plane and the loop parameter is a good quantum number similar to a momentum. All eigenstates are subexponentially `localized', i.e. the logarithm of the absolute value of the wave function performs a random walk in space, and are characterized by a corresponding length scale $ξ_{sel}$ as shown in 1998 by Silvestrov for the general Hatano-Nelson chain. For $M=2$ real-valued binary disorder with equal weights the model was solved in Zeitschrift für Naturforschung A 81 421, yielding Cassini oval spectral loops and a diverging subexponential localization length for two eigenstates and for disorder weaker than a critical value set by the hopping strength. When the disorder field for any $M$ and arbitrary weights is confined to circles in the complex plane with radius equal to the hopping strength, the circle center will belong to the spectrum and to one of the spectral loops, and host a plane-wave-like eigenstate with diverging $ξ_{sel}$. We generalize to tailoring on-site disorder for a given eigenstate at a given energy, for any lattice dimension, and any hopping field (both ordered and disordered), for Hermitian and non-Hermitian systems. We exemplify by constructing a one-dimensional chain with Anderson-localized eigenstates hosting a completely delocalized one with random phases. The localization length diverges as $1/|E|^{2/3}$ upon approaching the delocalized state. Our method can be used for the systematic construction of disorder fields which host predefined eigenstates with arbitrary properties.
