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

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 $T\ge T_c$. 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.

4 pages, 2 figures

References in corpus (4)

• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Entanglement entropy in collective models
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states

Cited by in corpus (3)

• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Optimal transport and von Neumann entropy in an Heisenberg XXZ chain out of equilibrium
• Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems