Perturbation study on the spin and charge susceptibilities of the two-dimensional Hubbard model

TL;DR

This study analyzes how spin and charge susceptibilities in the 2D Hubbard model change with interaction strength and doping, revealing behaviors related to Mott-Hubbard gap formation and spin-gap phenomena.

Contribution

It provides a perturbative analysis including vertex corrections, highlighting behaviors not captured by simpler approximations like RPA.

Findings

Charge susceptibility decreases near half-filling with hole-doping.

Spin susceptibility shows a spin-gap-like decrease at low temperatures.

Vertex corrections are essential for capturing Mott-Hubbard gap precursors.

Abstract

We investigate the spin and charge susceptibilities of the two-dimensional Hubbard model based upon the perturbative calculation in the strength of correlation $U$. For $U$ comparable to a bare bandwidth, the charge susceptibility decreases near the half-filling as hole-doping approaches zero. This behavior suggesting the precursor of the Mott-Hubbard gap formation cannot be obtained without the vertex corrections beyond the random phase approximation. In the low-temperature region, the spin susceptibility deviates from the Curie-Weiss-like law and finally turns to decrease with the decrease of temperature. This spin-gap-like behavior is originating from the van Hove singularity in the density of states.