Entanglement entropy in quantum impurity systems and systems with boundaries

TL;DR

This paper reviews how quantum impurities and boundaries influence entanglement entropy in various systems, highlighting recent analytical and theoretical advances, especially in one-dimensional models and their connection to topological entropy.

Contribution

It provides a comprehensive review of impurity and boundary effects on entanglement entropy, including new results and analytical approaches in 1+1 dimensional systems.

Findings

Analytical results for entanglement entropy in conformally invariant boundary conditions

Connection between impurity entanglement and topological entropy

New results for systems with mixed boundary conditions

Abstract

We review research on a number of situations where a quantum impurity or a physical boundary has an interesting effect on entanglement entropy. Our focus is mainly on impurity entanglement as it occurs in one dimensional systems with a single impurity or a boundary, in particular quantum spin models, but generalizations to higher dimensions are also reviewed. Recent advances in the understanding of impurity entanglement as it occurs in the spin-boson and Kondo impurity models are discussed along with the influence of boundaries. Particular attention is paid to 1+1 dimensional models where analytical results can be obtained for the case of conformally invariant boundary conditions and a connection to topological entanglement entropy is made. New results for the entanglement in systems with mixed boundary conditions are presented. Analytical results for the entanglement entropy obtained from Fermi liquid theory are also discussed as well as several different recent definitions of the impurity contribution to the entanglement entropy.