Localization phenomena in the random XXZ spin chain

TL;DR

This paper demonstrates that the random XXZ spin chain exhibits localization phenomena such as spectral and eigenstate localization across a broad parameter space, using decay properties of Green functions to establish these results.

Contribution

It proves localization in the infinite random XXZ spin chain by linking finite volume Green function decay to infinite volume decay, extending previous finite system results.

Findings

Spectral localization in the random XXZ chain

Eigenstate localization confirmed for the model

Weak dynamical localization established

Abstract

It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of the parameter space. This region depends only on the energy interval and includes weak interaction and strong disorder regimes. The crucial step in the argument is a proof that if the Green functions for the associated finite systems Hamiltonians exhibit certain (volume-dependent) decay properties in a fixed energy interval, then the infinite volume Green function decays in the same interval as well. The pertinent finite systems decay properties for the random XXZ spin chain had been previously verified by the authors.