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The multiorbital Hubbard model is expressed in terms of quantum phasevariables (``slave rotors'') conjugate to the local charge, and of auxiliaryfermions, providing an economical representation of the Hilbert space ofstrongly correlated systems. When the phase variables are treated in a localmean-field manner, similar results to the dynamical mean-field theory areobtained, namely a Brinkman-Rice transition at commensurate fillings togetherwith a ``preformed'' Mott gap in the single-particle density of states. Theslave- rotor formalism allows to go beyond the local description and take intoaccount spatial correlations, following an analogy to the superfluid-insulatortransition of bosonic systems. We find that the divergence of the effectivemass at the metal- insulator transition is suppressed by short range magneticcorrelations in finite-dimensional systems. Furthermore, the strict separationof energy scales between the Fermi- liquid coherence scale and the Mott gapfound in the local picture, holds only approximately in finite dimensions, dueto the existence of low-energy collective modes related to zero-sound.Comment: 16 pages, 12 figure

Slave-rotor mean-field theories of strongly correlated systems and the Mott transition in finite dimensions