Dynamical Localization in Disordered Quantum Spin Systems

TL;DR

This paper investigates dynamical localization in disordered quantum spin systems, establishing links between localization and correlation decay, and analyzing specific models like the random xy spin chain.

Contribution

It introduces a rigorous definition of dynamical localization in quantum spin systems and connects it to correlation decay and effective one-particle Hamiltonians.

Findings

Dynamical localization implies exponential decay of ground state correlations.

Localization in random xy chains can be analyzed via effective one-particle Hamiltonians.

The isotropic xy chain in a random magnetic field exhibits dynamical localization.

Abstract

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.