Renormalization group calculation of the uniform susceptibilities in low-dimensional systems

TL;DR

This paper employs a two-loop renormalization group approach to analyze uniform susceptibilities in low-dimensional Hubbard models, revealing metallic behavior in 1D and insulating tendencies in 2D, supporting the spin liquid hypothesis.

Contribution

It introduces a two-loop RG scheme for susceptibilities in low-dimensional systems and compares it with RPA, providing new insights into the insulating nature of 2D Hubbard models.

Findings

1D Hubbard model shows Luttinger liquid behavior.

2D Hubbard model susceptibilities are suppressed near the Fermi surface.

Comparison between two-loop RG and RPA schemes clarifies their differences.

Abstract

We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behavior of two central quantities of a system: the uniform charge and spin susceptibilities. We point out that a consistent renormalization group treatment of them can only be achieved within a two-loop approach or beyond. In the 1D HM, we show that this scheme reproduces correctly the metallic behavior given by the well-known Luttinger liquid fixed-point result. Then, we use the same approach to deal with the more complicated 2D HM. In this case, we are able to show that both uniform susceptibilities become suppressed for moderate interaction parameters as one take the system towards the Fermi surface. Therefore, this result adds further support to the interpretation that those systems are in fact insulating spin liquids. Later, we perform the same calculations in 2D using the conventional random phase approximation, and establish clearly a comparison between the two schemes.