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

TL;DR

This paper investigates the real-time dynamics of typical and untypical states in non-integrable spin chains, examining how initial state properties influence diffusion and non-equilibrium behavior beyond integrable models.

Contribution

It extends previous studies on integrable systems to non-integrable models, analyzing the effects of initial state typicality and entanglement on dynamics.

Findings

Diffusive behavior depends on initial state typicality.

Differences in dynamics linked to entanglement and local density of states.

Non-integrable models show varied non-equilibrium responses.

Abstract

For a class of typical states, the real-time and real-space dynamics of non-equilibrium density profiles has been recently studied for integrable models, i.e. the spin-1/2 XXZ chain [PRB 95, 035155 (2017)] and the Fermi-Hubbard chain [PRE 96, 020105 (2017)]. It has been found that the non-equilibrium dynamics agrees with linear response theory. Moreover, in the regime of strong interactions, clear signatures of diffusion have been observed. However, this diffusive behavior strongly depends on the choice of the initial state and disappears for untypical states without internal randomness. In the present work, we address the question whether or not the above findings persist for non-integrable models. As a first step, we study the spin-1/2 XXZ chain, where integrability can be broken due to an additional next-nearest neighbor interaction. Furthermore, we analyze the differences of typical and untypical initial states on the basis of their entanglement and their local density of states.