Entanglement entropy and localization in disordered quantum chains

TL;DR

This paper reviews and presents new results on quantum entanglement entropy in disordered quantum chains, focusing on Anderson localization, infinite randomness criticality, and many-body localization, highlighting their distinct entanglement properties.

Contribution

It provides a comprehensive review and new insights into entanglement entropy behavior across different disordered quantum phases and energy regimes.

Findings

Entanglement entropy varies significantly across localized and critical phases.

New results on entanglement entropy at low and high energies in random spin chains.

Comparison of entanglement properties in Anderson, critical, and MBL systems.

Abstract

This chapter addresses the question of quantum entanglement in disordered chains, focusing on the von-Neumann and R\'enyi entropies for three important classes of random systems: Anderson localized, infinite randomness criticality, and many-body localization (MBL). We review previous works, and also present new results for the entanglement entropy of random spin chains at low and high energy.