We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model at weak correlation strength by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.
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