title: Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
abstract: Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n>>1. As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T. The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T≥Tc, is demonstrated.
authors.affiliation: Dipartimento di Fisica ER Caianiello, CNISM and INFN-Gruppo Collegato di Salerno, via Ponte don Melillo, I-84084 Fisciano, SA, Italy.
authors.forename: Mario
authors.initials: M
authors.lastname: Salerno
authors.forename: Vladislav
authors.initials: V
authors.lastname: Popkov