Antiferromagnetic fluctuations in the one-dimensional Hubbard model

TL;DR

This paper investigates the critical behavior of the one-dimensional Hubbard model near half filling, focusing on antiferromagnetic fluctuations and their evolution across temperature and interaction strength using a mean-field approach.

Contribution

It introduces a mean-field-type approximation with two-particle self-consistency to analyze the crossover from weak to strong coupling and the approach to a quantum critical point.

Findings

Identification of a crossover temperature $T_0$ depending on interaction strength

Diverging staggered susceptibility near the quantum critical point

Development of a gap in the excitation spectrum at zero temperature

Abstract

We study the low-temperature critical behavior of the one-dimensional Hubbard model near half filling caused by enhanced antiferromagnetic fluctuations. We use a mean-field-type approximation with a two-particle self-consistency renormalizing the bare interaction. It allows us to control a transition from high to low temperatures as well as from weak to strong-coupling. We show that there is a crossover temperature $T_{0}= t\exp\{-1/U\rho(0)\}$ for arbitrary interaction $U>0$ and the bare density of states at the Fermi energy $\rho(0)>0$. The solution at lower temperatures goes over to strong coupling and approaches a quantum critical point with the diverging staggered susceptibility and a gap in the excitation spectrum at zero temperature.