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 "quasiparticle" 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.