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

TL;DR

This paper investigates how next-nearest-neighbor hopping influences charge collective modes in the Hubbard model's paramagnetic phase, revealing significant effects on mode velocities and damping, with results aligning with quantum Monte Carlo simulations.

Contribution

It provides a detailed analysis of the impact of next-nearest-neighbor hopping on charge collective modes using Gaussian fluctuations in the slave-boson framework, highlighting differences from RPA and agreement with QMC.

Findings

Negative t'/t decreases zero-sound velocity at positive doping.

Next-nearest-neighbor hopping affects damping and mode softening/hardening.

Results differ from RPA but agree with quantum Monte Carlo simulations.

Abstract

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 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.