  It has been proposed that the states of fully many-body localized systems can
be described in terms of conserved local pseudospins. Due to the multitude of
ways to define these, the explicit identification of the optimally local
pseudospins in specific systems is non-trivial. Given continuing intense
interest in the role of disorder in strongly correlated systems, we consider
the disordered Hubbard model. Focusing on a two-site system, we track the
evolution of the optimally localized pseudospins as hopping and interactions
are varied to move the system away from the trivially localized atomic limit,
examining the explicit form of the pseudospins and exploring the broad
distribution of non-optimal forms.
