Issue
EPL
Volume 84, Number 3, November 2008
Article Number 30007
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/30007
Published online 28 October 2008
EPL, 84 (2008) 30007
DOI: 10.1209/0295-5075/84/30007

Scaling of the von Neumann entropy across a finite-temperature phase transition

V. Popkov and M. Salerno

Dipartimento di Fisica “E.R. Caianiello" and Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia (CNISM), Università di Salerno - I-84081, Baronissi (SA), Italy, EU

salerno@sa.infn.it

received 26 July 2008; accepted in final form 24 September 2008; published November 2008
published online 28 October 2008

Abstract
The spectrum of the reduced density matrix and the temperature dependence of the von Neumann entropy (VNE) are analytically obtained for a system of hard-core bosons on a complete graph which exhibits a phase transition to a Bose-Einstein condensate at T = Tc. It is demonstrated that the VNE undergoes a crossover from purely logarithmic at T = 0 to purely linear in block size n behaviour for T $\geqslant$ Tc. For intermediate temperatures, VNE is a sum of two contributions which are interpreted as the classical (Gibbs) and the quantum (due to entanglement) parts of the von Neumann entropy.

PACS
03.67.Mn - Entanglement measures, witnesses, and other characterizations.
03.75.Gg - Entanglement and decoherence in Bose-Einstein condensates.
87.15.Zg - Phase transitions.

© EPLA 2008