Motivated by recent studies of circuit complexity in weakly interacting
scalar field theory, we explore the computation of circuit complexity in
$\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We
consider a massive free field theory with higher-order Wilsonian operators such
as $\phi^{4}$, $\phi^{6}$ and $\phi^8.$ To facilitate our computation we
regularize the theory by putting it on a lattice. First, we consider a simple
case of two oscillators and later generalize the results to $N$ oscillators.
The study has been carried out for nearly Gaussian states. In our computation,
the reference state is an approximately Gaussian unentangled state, and the
corresponding target state, calculated from our theory, is an approximately
Gaussian entangled state. We compute the complexity using the geometric
approach developed by Nielsen, parameterizing the path ordered unitary
transformation and minimizing the geodesic in the space of unitaries. The
contribution of higher-order operators, to the circuit complexity, in our
theory has been discussed. We also explore the dependency of complexity with
other parameters in our theory for various cases.
