| Issue |
EPL
Volume 84, Number 3, November 2008
|
|
|---|---|---|
| Article Number | 30007 | |
| Number of page(s) | 5 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/84/30007 | |
| Published online | 28 October 2008 | |
Scaling of the von Neumann entropy across a finite-temperature phase transition
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
Corresponding author: salerno@sa.infn.it
Received:
26
July
2008
Accepted:
24
September
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.
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
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