title: Excited-state quantum phase transitions in the two-spin elliptic Gaudin model.
abstract: We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems.
authors.affiliation: Departamento de Física Aplicada I and GISC, Universidad Complutense de Madrid, Avenida Complutense s/n, 28040 Madrid, Spain.
authors.forename: Armando
authors.initials: A
authors.lastname: Relaño
authors.affiliation: Departamento de Física y Matemáticas, Universidad de Alcalá, E-28871 Alcalá de Henares, Spain.
authors.forename: Carlos
authors.initials: C
authors.lastname: Esebbag
authors.affiliation: Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas, Serrano 123, E-28006 Madrid, Spain.
authors.forename: Jorge
authors.initials: J
authors.lastname: Dukelsky