title: Entanglement and classical instabilities: fingerprints of electron-hole-to-exciton phase transition in a simple model.
abstract: We propose a schematic model to study the formation of excitons in bilayer electron systems. The phase transition is signalized both in the quantum and classical versions of the model. In the present contribution we show that not only the quantum ground state but also higher energy states, up to the energy of the corresponding classical separatrix orbit, "sense" the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for a given quantum state and the behavior of the corresponding classical orbit.
authors.affiliation: Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil. tathiana@fisica.ufmg.br
authors.forename: Tathiana
authors.initials: T
authors.lastname: Moreira
authors.forename: Giancarlo Q
authors.initials: GQ
authors.lastname: Pellegrino
authors.forename: J G
authors.initials: JG
authors.lastname: Peixoto de Faria
authors.forename: M C
authors.initials: MC
authors.lastname: Nemes
authors.forename: F
authors.initials: F
authors.lastname: Camargo
authors.forename: A F R
authors.initials: AF
authors.lastname: de Toledo Piza