Sunday, August 4, 2013

1308.0277 (Maurizio Fagotti)

Dynamical Phase Transitions as Properties of the Stationary State:
Analytic Results after Quantum Quenches in the Spin-1/2 XXZ Chain

Maurizio Fagotti
The (Loschmidt) overlap between the state at different times after a quantum quench is attracting increasing interest, as it was recently shown to have a non-analytic behavior if a Hamiltonian parameter is quenched across a critical point. This phenomenon was called a "dynamical phase transition" in analogy with the behavior of the canonical partition function at an equilibrium phase transition. We consider the nonequilibrium time evolution with the Hamiltonian of the XXZ spin-1/2 chain and derive a general expression for the Loschmidt amplitude. We represent the state that describes the stationary properties of (local) observables as a Gibbs ensemble of a generalized Hamiltonian. By analyzing the large time behavior of the overlap, we reveal a deep connection between the appearance of singularities and the spectral properties of the generalized Hamiltonian.
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