Ballistic spreading of entanglement in a diffusive nonintegrable system

TL;DR

This paper demonstrates that in a nonintegrable quantum spin chain, entanglement spreads ballistically at a faster rate than energy diffuses, highlighting a fundamental difference in dynamical behaviors.

Contribution

The study provides the first explicit evidence that entanglement spreads ballistically in a nonintegrable system, contrasting with diffusive energy transport.

Findings

Entanglement entropy increases linearly with time before saturation.

Energy transport remains diffusive despite ballistic entanglement spreading.

Entanglement spreads faster than energy in the studied system.

Abstract

We study the time evolution of the entanglement entropy of a one-dimensional nonintegrable spin chain, starting from random nonentangled initial pure states. We use exact diagonalization of a nonintegrable quantum Ising chain with transverse and longitudinal fields to obtain the exact quantum dynamics. We show that the entanglement entropy increases linearly with time before finite-size saturation begins, demonstrating a ballistic spreading of the entanglement, while the energy transport in the same system is diffusive. Thus we explicitly demonstrate that the spreading of entanglement is much faster than the energy diffusion in this nonintegrable system.