Symmetries and Delocalization in the Disordered Hubbard Model

Many-body localization is believed to be generically unstable in quantum systems with continuous non-Abelian symmetries, even in the presence of strong disorder. Breaking these symmetries can stabilise the localized phase, leading to the emergence of an extensive number of quasi-locally conserved quantities known as local integrals of motion, or l-bits. Using a sophisticated non-perturbative technique based on continuous unitary transforms, we investigate the one-dimensional Hubbard model subject to both spin and charge disorder, compute the associated l-bits and demonstrate that the disorder gives rise to a novel form of spin-charge separation. We examine the role of symmetries in delocalizing the spin and charge degrees of freedom, and show that while symmetries generally lead to delocalization through multi-particle resonant processes, certain subsets of states appear stable.