title: Dynamical phase transitions and Loschmidt echo in the infinite-range XY model.
abstract: We compare two different notions of dynamical phase transitions in closed quantum systems. The first is identified through the time-averaged value of the equilibrium-order parameter, whereas the second corresponds to non-analyticities in the time behaviour of the Loschmidt echo. By exactly solving the dynamics of the infinite-range XY model, we show that in this model non-analyticities of the Loschmidt echo are not connected to standard dynamical phase transitions and are not robust against quantum fluctuations. Furthermore, we show that the existence of either of the two dynamical transitions is not necessarily connected to the equilibrium quantum phase transition.
authors.affiliation: Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, Trieste, Italy.
authors.forename: Bojan
authors.initials: B
authors.lastname: Žunkovič
authors.affiliation: Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, Trieste, Italy asilva@sissa.it.
authors.forename: Alessandro
authors.identifier: http://orcid.org/0000-0002-5668-7134
authors.initials: A
authors.lastname: Silva
authors.affiliation: Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, Trieste, Italy.
authors.forename: Michele
authors.initials: M
authors.lastname: Fabrizio
keywords: Loschmidt echo; non-equilibrium; quantum phase transitions