Luttinger Sum Rule in Slave-Particle Theories

TL;DR

This paper demonstrates that, contrary to common belief, the Luttinger sum rule can be preserved in slave-particle theories when the mean-field approximation is applied consistently, using the Emery model as an example.

Contribution

It shows that the Luttinger sum rule is not necessarily violated in slave-particle approaches if the mean-field procedure is applied properly to both the Hamiltonian and propagators.

Findings

The sum rule is restored with consistent mean-field application.

The electron spectrum includes a large number of states at the ion's bare energy.

The results are generalizable to similar strongly correlated systems.

Abstract

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.