Effect of the next-nearest-neighbor hopping on the charge collective modes in the paramagnetic phase of the Hubbard model - Archive ouverte HAL Access content directly
Journal Articles EPL - Europhysics Letters Year : 2017

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

Vu Hung Dao

#### 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.

### Dates and versions

hal-02333310 , version 1 (25-10-2019)

### Identifiers

• HAL Id : hal-02333310 , version 1
• DOI :

### Cite

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, 2017, 120 (1), pp.17004. ⟨10.1209/0295-5075/120/17004⟩. ⟨hal-02333310⟩

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