Ruelle-Pollicott spectrum and non-hydrodynamic correlators in a U(1) symmetric Floquet circuit

The decay of temporal correlation functions is central topic in the study of many-body quantum dynamics. One way to compute these decay constants, which has seen recent renewed interest, is as Ruelle-Pollicott (RP) resonances: eigenmodes of the dissipative propagator with dissipation taken to zero after the thermodynamic limit. In certain Floquet systems with no symmetries, it has been shown that isolated resonances capture the exponential decay of correlators. With an added U(1) symmetry, the momentum dependence of the RP spectrum is shown to capture the hydrodynamic behavior. However, a recent study [E. McCulloch et al., arXiv:2504.05380 (2025)] argued that operators orthogonal to the U(1) hydrodynamic modes will decay in time as a stretched exponential, which has yet to be reconciled with RP resonances. In this work, we investigate the behavior of the RP spectrum for these non-hydrodynamic modes using a novel matrix product operator (MPO) implementation of the RP procedure. In particular, we implement the dissipation using a translationally invariant operator truncation scheme [T. Prosen, J. Phys. A: Math. Theor. 40, 7881 (2007)]. This approach allows us to numerically achieve large truncation sizes, corresponding to weak dissipation, which provides significantly improved convergence and allows us to characterize the non-hydrodynamic decays present.