# 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 $t\mbox{-}t'\mbox{-}U$ 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 $t'/t$ 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.
Document type :
Journal articles

https://hal-normandie-univ.archives-ouvertes.fr/hal-02333310
Contributor : Raymond Frésard Connect in order to contact the contributor
Submitted on : Friday, October 25, 2019 - 11:56:44 AM
Last modification on : Saturday, June 25, 2022 - 9:54:20 AM

### Citation

Vu Hung Dao, Raymond Fresard. Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2017, 120 (1), pp.17004. ⟨10.1209/0295-5075/120/17004⟩. ⟨hal-02333310⟩

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