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

Abstract

The charge dynamical response function of the $t-t^{\prime }-U$ 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 slightly affects the renormalization of the quasiparticle mass. In contrast a negative $t^{\prime }/t$ notably decreases (increases) their velocity, and hence the zero-sound velocity, at positive (negative) doping. For low (high) density $n\lesssim 0.5$ ($n\gtrsim 1.5$) we find 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. It is also shown that our results differ markedly from the random phase approximation in the strong-coupling limit, even at high doping, while they compare favorably with existing quantum Monte Carlo numerical simulations.

arXiv comment7 pages, 4 figures

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