Attaining the maximum Bose-Einstein condensation in a finite-size hard-core boson model

Abstract

We propose a model for hard-core bosons in a lattice which allows toachieve the optimal occupation number predicted by Tennie et al. [Tennie F, VedralV, and Schilling C 2017 Phys. Rev. B 96 064502] for a finite number of sites. Themodel is based on an extension of the Hamiltonian of the so-called Hubbard star, whosequantum properties are studied by means of quantum information descriptors such asthe von Neumann entropy and the mutual information. These metrics are analysed as afunction of the one- and two-particle reduced density matrices, allowing to explore therelationship between condensation and entanglement by means of a control parameterthat, under a given limit, connects our findings with previous results. All developmentscomprised in this article have been derived by analytical methods.