Circuit Complexity in Z2 EEFT

Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in (Formula presented.) Even Effective Field Theories ((Formula presented.) EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as (Formula presented.), (Formula presented.), and (Formula presented.) 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. This study was 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 is discussed. We also explore the dependency of complexity on other parameters in our theory for various cases.