Universality of equilibration dynamics after quantum quenches

TL;DR

This paper demonstrates that the lower part of the entanglement spectrum after a quantum quench exhibits universal behavior, with the distribution depending on parameters derived from Re9nyi entropies, across various models.

Contribution

It reveals the universality of the entanglement spectrum distribution after quantum quenches and characterizes two distinct scenarios with analytical and numerical benchmarks.

Findings

Two universal regimes of entanglement spectrum distribution identified.

Distribution depends on parameters from Re9nyi entropies.

Analytical results validated in multiple integrable models.

Abstract

We investigate the distribution of the eigenvalues of the reduced density matrix (entanglement spectrum) after a global quantum quench. We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits ``universality''. In the scaling limit and at asymptotically long times the distribution of the entanglement spectrum depends on two parameters that can be determined from the R\'enyi entropies. We show that two typical scenarios occur. In the first one, the distribution of the entanglement spectrum levels is similar to the one describing the ground-state entanglement spectrum in Conformal Field Theories. In the second scenario, the lower levels of the entanglement spectrum are highly degenerate and their distribution is given by a series of Dirac deltas. We benchmark our analytical results in free-fermion chains, such as the transverse field Ising chain and the XX chain, in the rule 54 chain, and in Bethe ansatz solvable spin models.