Luttinger Sum Rule in Slave-Particle Theories

The long-standing belief is that the mean-field-like decoupling procedures applied to the slave-particle representations of the problems with strong local interaction violate Luttinger sum rule. The number of occupied resonant states is small and typically equal to the deviation from the sum rule, shedding doubt on the overall results. It is therefore illustrated, on the example of the Emery model for the high-Tc superconductors, that, through the consistent application of the mean-field procedure to the Hamiltonian and the propagators, the sum rule is restored and the resonant band conserved. In addition to the resonant band, the electron spectrum contains large number of occupied states at the bare site-energy of the ion with strong repulsion. These results can be straightforwardly generalized to the other similar problems.