Power-law entanglement growth from typical product states

TL;DR

This paper demonstrates a power-law growth of entanglement entropy in quantum many-body systems from typical product states, linking wave function complexity and operator entanglement, especially under disorder and in ergodic regimes.

Contribution

It establishes a robust correspondence between wave function entanglement growth and operator entanglement, revealing power-law dynamics in disordered systems and clarifying previous discrepancies.

Findings

Power-law entanglement growth in disordered spin chains

Correlation between wave function and operator entanglement growth

Evidence for slow information spreading near many-body localization transition

Abstract

Generic quantum many-body systems typically show a linear growth of the entanglement entropy after a quench from a product state. While entanglement is a property of the wave function, it is generated by the unitary time evolution operator and is therefore reflected in its increasing complexity as quantified by the operator entanglement entropy. Using numerical simulations of a static and a periodically driven quantum spin chain, we show that there is a robust correspondence between the entanglement entropy growth of typical product states with the operator entanglement entropy of the unitary evolution operator, while special product states, e.g. $\sigma_z$ basis states, can exhibit faster entanglement production. In the presence of a disordered magnetic field in our spin chains, we show that both the wave function and operator entanglement entropies exhibit a power-law growth with the same disorder-dependent exponent, and clarify the apparent discrepancy in previous results. These systems, in the absence of conserved densities, provide further evidence for slow information spreading on the ergodic side of the many-body localization transition.