Quantum quenches with random matrix Hamiltonians and disordered potentials

TL;DR

This paper explores how quantum quenches in disordered systems and sparse random matrices lead to statistical ensembles that can sometimes exhibit condensation phenomena, with implications for understanding localization and delocalization.

Contribution

It introduces a comparison between quench-induced ensembles and the quantum micro-canonical ensemble, revealing conditions under which condensation occurs and providing insights into localization probabilities.

Findings

Condensation phenomenon occurs in certain sparse random matrix quenches.

Qualitative agreement with QMC predictions generally, with some cases of quantitative accuracy.

QMC ensemble helps estimate localization versus delocalization probabilities.

Abstract

We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching-on the off-diagonal elements of the Hamiltonian. In the latter case, it is sudden switching-on of the hopping between adjacent lattice sites. The quench-induced ensembles are compared with the so-called "quantum micro-canonical" (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.