Eur. Phys. J. B 64, 321-326 (2008)
https://doi.org/10.1140/epjb/e2008-00102-5

Entanglement entropy in extended quantum systems

Rudolph Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK and All Souls College, Oxford, UK

Corresponding author: ^a j.cardy1@physics.ox.ac.uk

Received: 22 August 2007
Revised: 14 February 2008
Published online: 12 March 2008

Abstract

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of freedom in different regions of space. Close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. In the second part I consider the unitary time evolution of such systems following a `quantum quench' in which a parameter in the Hamiltonian is suddenly changed, and argue that finite regions should effectively thermalise at late times, after interesting transient effects.