We study a one-dimensional Fermi-Hubbard model with disorder in charge and spin degrees of freedom. We calculate the time dependence of the entanglement entropy. While previous research on disordered interacting systems has typically focused on systems with either charge or spin, our model enables us to explore the interplay between charge and spin in shaping the behavior of entanglement. We use a method that identifies optimally local charge- and spin-specific integrals of motion. We ask how the locality level of these integrals of motion influences the capacity of low-order terms in the l-bit Hamiltonian to capture the entanglement entropy. Our results show that increasing the locality level improves the accuracy of low-order terms in capturing entanglement entropy dynamics. With equally strong charge and spin disorder, the behavior of the entanglement entropy closely resembles that observed in single-degree-of-freedom systems, and the l-bit Hamiltonian truncated at second order accurately captures this behavior.
Author Keywords: Entanglement Entropy, Fermi-Hubbard Model, Hungarian Algorithm, l-bit Hamiltonian, Local Integrals of Motion, Many-Body Localization