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

TL;DR

Adding a boundary term to an Anderson localized Hamiltonian causes unbounded entanglement growth, indicating that Anderson localization is not purely a local property and can be influenced by distant system parts.

Contribution

This work demonstrates that a single boundary term can destroy Anderson localization, revealing its non-local nature and challenging previous assumptions.

Findings

Boundary terms induce unbounded entanglement growth.

Anderson localization is not solely a local property.

Subsystem behavior can be affected by distant boundary modifications.

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.