Scaling of the von Neumann entropy across a finite-temperature phase transitionV. 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
received 26 July 2008; accepted in final form 24 September 2008; published November 2008
published online 28 October 2008
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 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.
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