Localization for random block operators related to the XY spin chain

TL;DR

This paper proves dynamical localization at non-zero energy for a class of random block operators modeling the XY quantum spin chain with random magnetic fields, advancing understanding of quantum localization phenomena.

Contribution

It establishes dynamical localization for random block operators associated with the XY spin chain under broad conditions, a novel result in quantum spin system analysis.

Findings

Proves dynamical localization at non-zero energies.

Applies to arbitrary non-trivial single-site distributions.

Enhances understanding of quantum localization in spin chains.

Abstract

We study a class of random block operators which appear as effective one-particle Hamiltonians for the anisotropic XY quantum spin chain in an exterior magnetic field given by an array of i.i.d. random variables. For arbitrary non-trivial single-site distribution of the magnetic field, we prove dynamical localization of these operators at non-zero energy.