Width of the generalized local density of states as an indicator of localization transition in interacting quantum systems

Motivated by generalized quantities that are useful for studying localization and multifractality within the context of many-body localization, we recently introduced the generalized survival probability (GSP) [1]. The GSP emphasizes contributions from all possible energy eigenstates by varying a single parameter, q. In the short-time regime, the GSP exhibits a quadratic decay characterized by the width σ_q of the generalized local density of states (GLDoS). The GLDoS has previously been interpreted as the escort probability distribution function [2] associated with the work done during a quantum quench in the integrable Luttinger model. In this work, we explore the generalized width in models commonly used for studying many-body localization.

[1] D. A. Zarate-Herrada, L. F. Santos, and E. J. Torres-Herrera, Entropy 25,205 (2023).

[2] C. Beck, F. Schlogel, and Y. L. Klimontovich, Physics-Uspekhi 37, 713 (1994).