Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement

Center for Theoretical Physics, Massachusetts Institute of Technology - Cambridge, MA 02139, USA

^(a) E-mail: yichenhuang@fas.harvard.edu (corresponding author)

Received: 12 December 2022
Accepted: 6 March 2023

Abstract

It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localization are lost.