Complexity Measure Diagnostics of Ergodic to Many-Body Localization Transition

TL;DR

This paper introduces complexity-based diagnostics using Lanczos coefficients to identify the transition between ergodic and many-body localized phases, providing new tools for analyzing quantum phase transitions.

Contribution

It presents novel complexity measures derived from Lanczos coefficients to diagnose ergodic to many-body localization transitions.

Findings

Complexity measures effectively distinguish phases.

Moments and entropy diagnose the transition.

Memory of initial conditions varies across phases.

Abstract

We introduce new diagnostics of the transition between the ergodic and many-body localization phases, which are based on complexity measures defined via the probability distribution function of the Lanczos coefficients of the tri-diagonalized Hamiltonian. We use these complexity measures to analyze the power-law random banded matrix model as a function of the correlation strength and show that the moments and the entropy of the distribution diagnose the ergodic to many-body transition, as well as the distinctive feature of the phases concerning the memory of the initial conditions.