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 Z2 Even Effective Field Theories (Z2 EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as 04, 06, and 08. 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.

Automated summary

Motivated by recent studies, this research explores the computation of circuit complexity in Z2 Even Effective Field Theories (Z2 EEFTs) in the context of weakly interacting scalar field theory. The complexity of a massive free field theory with higher-order Wilsonian operators is calculated, considering both the simple case of two oscillators and the general case of N oscillators. Geometric approach and parameterization techniques are used to compute the complexity, taking into account the contribution of higher-order operators and the dependency on other parameters.