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

The multiorbital Hubbard model is expressed in terms of quantum phase variables ("slave rotors") conjugate to the local charge, and of auxiliary fermions, providing an economical representation of the Hilbert space of strongly correlated systems. When the phase variables are treated in a local mean-field manner, similar results to the dynamical mean-field theory are obtained, namely a Brinkman-Rice transition at commensurate fillings together with a "preformed" Mott gap in the single-particle density of states. The slave-rotor formalism allows to go beyond the local description and take into account spatial correlations, following an analogy to the superfluid-insulator transition of bosonic systems. We find that the divergence of the effective mass at the metal-insulator transition is suppressed by short range magnetic correlations in finite-dimensional systems. Furthermore, the strict separation of energy scales between the Fermi-liquid coherence scale and the Mott gap, found in the local picture, holds only approximately in finite dimensions, due to the existence of low-energy collective modes related to zero-sound.