Thermalization dynamics in a glassy quantum circuit

Quantum circuits have emerged as a useful setting for studying quantum many-body systems. Random quantum circuits have been particularly useful in examining chaotic behavior in these systems and identifying its universal features. In this talk we present a random Floquet circuit model that is neither integrable nor fully chaotic, instead exhibiting glassy behavior. In general it quickly thermalizes within a sector of the state space but only fully thermalizes at a much later time, if at all. Using an effective field theory approach we determine the ensemble-averaged time evolution of the density matrix and the two-level correlation function. We demonstrate that these results indicate a glassy two-step thermalization process.