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arXiv · 0804.1061

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

Vladislav Popkov·Mario Salerno
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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 $T=T_c$. It is demonstrated that the VNE undergoes a crossover from purely logarithmic at T=0 to purely linear in block size $n$ behaviour for $T\geq T_{c}$. For intermediate temperatures, VNE is a sum of two contributions which are identified as the classical (Gibbs) and the quantum (due to entanglement) parts of the von Neumann entropy.

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Vladislav Popkov, Mario Salerno. 2008-04-07. Scaling of the von Neumann entropy across a finite temperature phase transition. https://doi.org/10.1209/0295-5075/84/30007

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