Connecting entanglement growth with local integrals of motion in the disordered Fermi Hubbard model

Generically a quantum system initialized in an unentangled state will, under unitary dynamics, rapidly become entangled, a process closely related to information transport and to thermalization. Disorder can suppress the growth of entanglement and result in memory of initial conditions. In non-interacting systems this arises from localization of single-particle states, the occupancy of which is fixed by the initial condition. In interacting systems similar conserved quantities persist, but with the added feature that they are coupled, resulting in entanglement growth which is distinct from both non-interacting localized systems and from generic ergodic systems. The Fermi Hubbard model has two degrees of freedom per site—charge and spin—and disorder may be present in both of these, with the same or differing strengths. We study this system by expanding the Hamiltonian in terms of a set of optimally localized conserved quantities with separate charge and spin character. This talk will examine the distribution of couplings between the conserved quantities and their connection with entanglement growth. We find much weaker coupling between charge and spin, relative to charge-charge and spin-spin coupling.