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

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.