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Abstract: The spectrum of the reduced density matrix and the temperature dependence ofthe von Neumann entropy VNE are analytically obtained for a system of hardcore bosons on a complete graph which exhibits a phase transition to aBose-Einstein condensate at $T=T c$. It is demonstrated that the VNE undergoesa 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 twocontributions which are identified as the classical Gibbs and the quantumdue to entanglement parts of the von Neumann entropy.



Author: Vladislav Popkov, Mario Salerno

Source: https://arxiv.org/







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