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Light-cone velocities after a global quench in a non-interacting model
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Abstract
We study the light-cone velocity for global quenches in the non-interacting XY chain starting from a class of initial states that are eigenstates of the local z-component of the spin. We point out how translation invariance of the initial state can affect the maximal speed at which correlations spread. As a consequence the light-cone velocity can be state-dependent also for non-interacting systems: a new effect of which we provide clear numerical evidence and analytic predictions. Analogous considerations, based on numerical results, are drawn for the evolution of the entanglement entropy.
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It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 (87)Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.
An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies of the problem have become possible, stimulating theoretical interest. In generic isolated systems, non-equilibrium dynamics is expected to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete. Some recent studies even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems. Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki. A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages-any eigenstate in the microcanonical energy window will do, because they all give the same result.
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