Title: Light cone velocities and revivals in a quantum spin chain
Abstract: Understanding the nonequilibrium dynamics of many-body quantum systems has become one of the most intriguing problems in condensed matter physics. Here, we study the simplest paradigm known as the quench problem for a quantum spin chain. One of the most successful descriptions is based on a quasi-particle picture where the maximum group velocity usually are the ones that can be connected to the saturation of the entanglement entropy or the revivals in the Loschmidt echo. Here, we show that in fact, the quasi-particles with different velocities can be important. We further show that these effective velocities are strongly dependent on different factors such as parameters of the Hamiltonian, the initial state and finally, they depend on to the observable that we study. To this end, first, we study the light-cone velocity for global quenches in the XY chain starting from a class of initial states. We point out how translation invariance of the initial state can affect the maximal speed at which correlations spread in the system and provide analytic predictions. Analogous considerations are drawn for the evolution of the entanglement entropy and the Loschmidt echo.