Subsystem complexity after a local quantum quench

Abstract

We study the temporal evolution of the circuit complexity after the local quench where two harmonic chains are suddenly joined, choosing the initial state as the reference state. We discuss numerical results for the complexity for the entire chain and the subsystem complexity for a block of consecutive sites, obtained by exploiting the Fisher information geometry of the covariance matrices. The qualitative behaviour of the temporal evolutions of the subsystem complexity depends on whether the joining point is inside the subsystem. The revivals and a logarithmic growth observed during these temporal evolutions are discussed. When the joining point is outside the subsystem, the temporal evolutions of the subsystem complexity and of the corresponding entanglement entropy are qualitatively similar.