Particle-hole symmetry of charge excitation spectra in the paramagnetic phase of the Hubbard model

TL;DR

This paper uses the Kotliar-Ruckenstein slave-boson approach to derive an analytical charge excitation spectrum in the Hubbard model's paramagnetic phase, revealing particle-hole symmetry and specific spectral features.

Contribution

It demonstrates that the analytical charge response function respects particle-hole symmetry on bipartite lattices within the slave-boson framework.

Findings

Charge spectra include a continuum, a gapless zero-sound mode, and a high-frequency mode at U.

The analytical expression obeys particle-hole symmetry on bipartite lattices.

The approach addresses formal aspects of the slave-boson method in this context.

Abstract

The Kotliar and Ruckenstein slave-boson representation of the Hubbard model allows to obtain an approximation of the charge dynamical response function resulting from the Gaussian fluctuations around the paramagnetic saddle-point in analytical form. Numerical evaluation in the thermodynamical limit yields charge excitation spectra consisting of a continuum, a gapless collective mode with anisotropic zero-sound velocity, and a correlation induced high-frequency mode at $\omega\approx U$. In this work we show that this analytical expression obeys the particle-hole symmetry of the model on any bipartite lattice with one atom in the unit cell. Other formal aspects of the approach are also addressed.