Each state in a one-dimensional disordered system has two localization lengths when the Hilbert space is constrained
Year: 2023
Type: preprint
Abstract: In disordered systems, the amplitudes of the localized states will decrease exponentially away from their centers and the localization lengths are characterizing such decreasing. In this article, we find a model in which each eigenstate is decreasing at two distinct rates. The model is a one-dimensional disordered system with a constrained Hilbert space: all eigenstates $|Ψ\rangle$s should be orthogonal to a state $|Φ\rangle$, $\langle Φ| Ψ\rangle =0$, where $|Φ\rangle$ is a given exponentially localized state. Although the dimension of the Hilbert space is only reduced by $1$, the amplitude of each state will decrease at one rate near its center and at another rate in the rest region, as shown in Fig. \ref{fig1}. Depending on $| Φ\rangle$, it is also possible that all states are changed from localized states to extended states. In such a case, the level spacing distribution is different from that of the three well-known ensembles of the random matrices. This indicates that a new ensemble of random matrices exists in this model. Finally we discuss the physics behind such phenomena and propose an experiment to observe them.
Source: arXiv (Cornell University)
Author: Xiong, Ye
Institution: Nanjing Normal University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4353007061