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Abstract

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.