Quantum entanglement in condensed matter systems

TL;DR

This review explores how quantum entanglement tools reveal complex properties of strongly correlated condensed matter systems, including topological order, disorder effects, and experimental measurement techniques.

Contribution

It provides a comprehensive overview of entanglement spectra, entropy, and their applications in diagnosing quantum states and phases in condensed matter physics.

Findings

Entanglement entropy obeys an area law with universal subleading corrections.

Entanglement spectrum can diagnose topological order and edge excitations.

Quantum entanglement techniques shed light on disordered systems like spin glasses and Kondo systems.

Abstract

This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated R\'enyi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in details. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.