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A prime characterization of many-body localized (MBL) systems is theentanglement of their eigenstates; in contrast to the typical ergodic phasewhose eigenstates are volume law, MBL eigenstates obey an area law. In thiswork, we show that a spin-disordered Hubbard model has both a large number ofarea-law eigenstates as well as a large number of eigenstates whoseentanglement scales logarithmically with system size (log-law). This model,then, is a microscopic Hamiltonian which is neither ergodic nor many-bodylocalized. We establish these results through a combination of analyticarguments based on the eta-pairing operators combined with a numerical analysisof eigenstates. In addition, we describe and simulate a dynamic time evolutionapproach starting from product states through which one can separately probethe area law and log-law eigenstates in this system.

Beyond many-body localized states in a spin-disordered Hubbard model with pseudo-spin symmetry