Particle-Hole Symmetry of Charge Excitation Spectra in the Paramagnetic Phase of the Hubbard Model
Résumé
The Kotliar and Ruckenstein slave-boson representation of the Hubbard model allows to obtain an approximation of the charge dynamical response function resulting from the Gaussian fluctuations around the paramagnetic saddle-point in analytical form. Numerical evaluation in the thermodynamical limit yields charge excitation spectra consisting of a continuum, a gapless collective mode with anisotropic zero-sound velocity, and a correlation induced high-frequency mode at omega approximate to U. In this work we show that this analytical expression obeys the particle-hole symmetry of the model on any bipartite lattice with one atom in the unit cell. Other formal aspects of the approach are also addressed.