Circuit Complexity in an interacting quenched Quantum Field Theory

Abstract: In this work, we explore the effects of a quantum quench on the circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. We use the invariant operator method, under a perturbative framework, for computing the ground state of this system}. We give the analytical expressions for specific reference and target states using the ground state of the system. Using a particular cost functional, we show the analytical computation of circuit complexity for the quenched and interacting field theory. Further, we give a numerical estimate of circuit complexity with respect to the quench rate, $\delta t$ for two coupled oscillators. The parametric variation of the unambiguous contribution of the circuit complexity for an arbitrary number of oscillators has been studied with respect to the dimensionless parameter $(t/\delta t$). We comment on the variation of circuit complexity for different values of coupling strength, different number of oscillators, and even in different dimensions.