Complexity as a novel probe of quantum quenches: universal scalings and purifications

Hugo A. Camargo, Pawel Caputa, Diptarka Das, Michal P. Heller, Ro Jefferson

Published 2018-07-18Version 1

We apply the recently developed notion of complexity for field theory to a quantum quench through the critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits universal scalings in both the slow and fast quench regimes. We then generalize our results to a 1-dimensional harmonic chain, and show that preservation of these scaling behaviours in free field theory depends on the choice of norm. Applying our set-up to the case of two oscillators, we quantify the complexity of purification associated to a subregion, and demonstrate that complexity is capable of probing features to which the entanglement entropy is insensitive. We find that the complexity of subregions is superadditive, and comment on potential implications for holography.