Entanglement entropy in one-dimensional disordered interacting system: The role of localization

TL;DR

This paper investigates how entanglement entropy behaves in one-dimensional disordered interacting systems, revealing that Anderson localization causes EE saturation and providing a heuristic model to relate EE to localization length and interaction strength.

Contribution

The study introduces a heuristic expression linking entanglement entropy to localization length, validated through numerical DMRG calculations, and explores the impact of interactions on localization.

Findings

Anderson localization causes EE saturation beyond the localization length.

A heuristic model describes EE dependence on localization length and finite size effects.

Localization length varies with interaction strength, matching theoretical expectations.

Abstract

The properties of the entanglement entropy (EE) in one-dimensional disordered interacting systems are studied. Anderson localization leaves a clear signature on the average EE, as it saturates on length scale exceeding the localization length. This is verified by numerically calculating the EE for an ensemble of disordered realizations using density matrix renormalization group (DMRG). A heuristic expression describing the dependence of the EE on the localization length, which takes into account finite size effects, is proposed. This is used to extract the localization length as function of the interaction strength. The localization length dependence on the interaction fits nicely with the expectations.