Quantum entanglement in condensed matter 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 Rényi 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.

Entanglement entropy of disordered quantum chains following a global quench

“…It is therefore of great interest to understand precisely how the entanglement depends on time following a quantum quench. While this question has already been studied extensively for clean systems, [11][12][13] disordered systems have only recently come into focus. [14][15][16][17] In such systems entanglement can, in addition, also provide a novel viewpoint to study localization.…”

Negativity in the generalized Valence Bond Solid state

“…Then, each virtual particle of spin S/2 is antisymmetrized with its nearest neighbor into the singlet state. The presence of this singlet between consecutive particles prevents the formation of total spin S i,i+1 = S i + S i+1 larger than S. Repeating this procedure with every particle in the chain, we obtain a state that is annihilated by the Hamiltonian (1). It corresponds to the groundstate of ( 1) with eigenvalue zero.…”

“…The use of quantum information concepts in the study and characterization of many-body systems has proved highly fruitful [1]. A clear example of such concepts is the entanglement entropy, which became an standard tool to characterize gapped, topological and critical phases [2][3][4][5].…”

Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality

“…In recent years entanglement measures have arisen as new diagnostic tools to unveil universal behaviors in quantum many-body systems. Arguably, the most popular and useful ones are the Rényi entropies and the von Neumann entropy [1][2][3][4] (entanglement entropies). Given a system in a pure state |ψ and a bipartition into an interval A and its complement (see Figure 1), the Rényi entropies S (n) A for part A are defined as…”