A uniform area law for the entanglement of eigenstates in the disordered XY chain

TL;DR

This paper proves that in disordered XY spin chains, eigenstate entanglement entropy obeys a uniform area law, indicating many-body localization across all energy levels, based on eigenfunction correlator localization.

Contribution

It establishes a connection between eigenfunction correlator localization and a uniform area law for entanglement entropy in disordered XY chains, extending many-body localization results.

Findings

Eigenfunction correlator localization implies a uniform area law for entanglement entropy.

The result applies to both isotropic and anisotropic XY chains with random fields.

The area law holds for all eigenstates, indicating many-body localization at all energies.

Abstract

We consider the isotropic or anisotropic XY spin chain in the presence of a transversal random magnetic field, with parameters given by random variables. It is shown that eigenfunction correlator localization of the corresponding effective one-particle Hamiltonian implies a uniform area law bound in expectation for the bipartite entanglement entropy of all eigenstates of the XY chain, i.e. a form of many-body localization at all energies. Here entanglement with respect to arbitrary connected subchains of the chain can be considered. Applications where the required eigenfunction correlator bounds are known include the isotropic XY chain in random field as well as the anisotropic chain in strong or strongly disordered random field.