Towards Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems

Due to controlled experiments with cold atomic gases and the development of sophisticated numerical methods, the study of non-equilibrium dynamics in many-body quantum systems has experienced an upsurge of interest. Particularly for closed systems, there has been immense theoretical effort to answer fundamental questions about equilibration and thermalization. Since such systems are isolated from their environment, out-of-equilibrium conditions can only be induced by the preparation of suitable initial states. In this context, we investigate the real-time dynamics for a class of non-equilibrium pure states in the spin-1/2 XXZ chain. Such states have been recently studied for integrable models [1,2], and relying on the concept of typicality, allow a comparison with results from linear response theory. By introducing an additional next-to-nearest neighbor interaction, we discuss the effect of integrability vs. non-integrability on the dynamics. Furthermore, the role of the specific initial state realization is analyzed in terms of internal randomness, entanglement entropy, and local density of states.

[1] R. Steinigeweg et al., Phys. Rev. B 95, 035155 (2017).

[2] R. Steinigeweg et al., Phys. Rev. E 96, 020105(R) (2017).

[3] J. Richter et al., in preparation.