The Luttinger sum rule in the slave-particle theories
Department of Physics, University of Zagreb, Bijenička 32, POB 331, 10002 Zagreb,
Corresponding author: a firstname.lastname@example.org
Revised: 2 July 2003
Published online: 9 September 2003
The usual mean field decoupling procedure applied to the slave-particle representations of the problems with strong local interaction produces a resonant band, but violates the Luttinger sum rule for the physical single-electron propagator. The number of occupied resonant states is small and equal to the deviation from the sum rule, shedding doubt on the overall results. It is therefore argued and 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 close to the bare site-energy of the site with strong repulsion. These results are also related here to the other similar decoupling problems, which also lead to the breakdown of the Luttinger sum rule.
PACS: 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003