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Using a recent proposal of circuit complexity in quantum field theoriesintroduced by Jefferson and Myers, we compute the time evolution of thecomplexity following a smooth mass quench characterized by a time scale $\deltat$ in a free scalar field theory. We show that the dynamics has two distinctphases, namely an early regime of approximately linear evolution followed by asaturation phase characterized by oscillations around a mean value. Thebehavior is similar to previous conjectures for the complexity growth inchaotic and holographic systems, although here we have found that thecomplexity may grow or decrease depending on whether the quench increases ordecreases the mass, and also that the time scale for saturation of thecomplexity is of order $\delta t$ (not parametrically larger).

Evolution of complexity following a quantum quench in free field theory