Localization and integrability breaking in weakly interacting Floquet circuits

We present a family of Floquet circuits that can interpolate between non-interacting qubits, free propagation, generic interacting, and dual-unitary dynamics. We identify the operator entanglement entropy of the two-qubit gate as a good quantitative measure of the interaction strength. We test the persistence of localization in the vicinity of the non-interacting point by probing spectral statistics, decay of autocorrelators, and measuring entanglement growth. The finite-size analysis suggests that the many-body localized regime does not persist in the thermodynamic limit. Instead, our results are compatible with an integrability-breaking phenomenon.