Entanglement Entropy in Extended Quantum Systems

TL;DR

This paper explores how entanglement entropy characterizes quantum correlations in many-body systems, especially near phase transitions and after quantum quenches, revealing universal features and thermalization behavior.

Contribution

It introduces the use of von Neumann entropy to analyze entanglement in extended quantum systems and discusses universal properties near phase transitions and during time evolution.

Findings

Entanglement entropy exhibits universal features near quantum phase transitions.

Finite regions tend to thermalize after a quantum quench.

Entanglement entropy effectively characterizes quantum correlations in many-body systems.

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.