Entanglement properties of the critical quench of O(N) bosons

TL;DR

This paper investigates the entanglement properties of critical $O(N)$ bosonic systems in three dimensions after a quantum quench, revealing how entanglement spectra reflect critical exponents and enabling their extraction through entanglement analysis.

Contribution

It provides the first detailed analysis of entanglement in 3D critical bosonic systems post-quench, combining numerical and analytical methods to connect entanglement spectra with critical exponents.

Findings

Entanglement entropy evolution is similar for free and interacting systems.

Low-lying entanglement spectrum is governed by different critical exponents.

Critical exponents can be extracted from entanglement spectra.

Abstract

The entanglement properties of quenched quantum systems have been studied for a decade, however results in dimensions other than $d=1$ are generally lacking. We remedy this by investigating the entanglement properties of bosonic critical systems in $d=3$, both numerically and analytically, comparing the free and the interacting critical quench of an $O(N)$ model. We find that the evolution of the entanglement entropy for these two systems is nearly identical, as expected from the "quasi-particle" picture. However, the low-lying entanglement spectrum is controlled by the different critical exponent of the two systems, and therefore these exponents may be extracted by purely entanglement-theoretic calculations. We verify this scaling numerically.