Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model

Abstract

Fd -Lattice fermion models PACS 72.15.Nj -Collective modes PACS 71.30.+h -Metal-insulator transitions and other electronic transitionsAbstract -The charge dynamical response function of the t−t ′ −U Hubbard model is investigated on the square lattice in the thermodynamical limit. The correlation function is calculated from Gaussian fluctuations around the paramagnetic saddle-point within the Kotliar and Ruckenstein slave-boson representation. The next-nearest-neighbor hopping only slighty affects the renormalisation of the quasiparticle mass. In contrast a negative t ′ /t notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density n 0.5 (n 1.5) we found that it enhances (reduces) the damping of the zero-sound mode. Furthermore it softens (hardens) the upper-Hubbard-band collective mode at positive (negative) doping. Our results are compared to existing numerical simulations.