Circuit Complexity in an interacting quenched Quantum Field Theory

TL;DR

This paper analytically and numerically investigates how quantum quenches affect circuit complexity in weakly interacting quantum field theories, revealing dependencies on quench rate, coupling strength, and system size.

Contribution

It introduces a perturbative method to compute circuit complexity in quenched interacting quantum fields and provides analytical and numerical insights into its behavior.

Findings

Circuit complexity varies with quench rate and coupling strength.

Analytical expressions for complexity in quenched systems are derived.

Numerical estimates show complexity dependence on system parameters.

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.