Using charge- and spin-specific local integrals of motion to explore entanglement growth in the disordered Fermi Hubbard model

The Fermi Hubbard model has both charge and spin degrees of freedom at each site. We explore the coupling of the dynamics in these two channels in the presence of disorder. In particular, we write the Hamiltonian in terms of charge- and spin-specific local integrals of motion, and compare the strengths of the coupling constants linking integrals of motion of the same species (charge-charge and spin-spin) with those linking charge and spin. This provides an avenue to understanding the wide range of time scales which appear in the dynamics.