Renormalization group analysis of the 2D Hubbard model

TL;DR

This paper applies a novel renormalization group method to the 2D Hubbard model, analyzing low-energy interactions and instabilities, revealing phases like antiferromagnetism and d-wave superconductivity depending on parameters.

Contribution

It extends Salmhofer's RG approach to compute susceptibilities and phase diagrams for the 2D Hubbard model, providing new insights into its low-energy behavior.

Findings

Diverging effective interactions indicate instabilities at small energy scales.

Identification of antiferromagnetic and d-wave superconducting phases.

Phase diagram near half-filling showing different dominant orders.

Abstract

Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new renormalization group method for interacting Fermi systems, where the complete flow from the bare action of a microscopic model to the effective low-energy action, as a function of a continuously decreasing infrared cutoff, is given by a differential flow equation which is local in the flow parameter. We apply this approach to the repulsive two-dimensional Hubbard model with nearest and next-nearest neighbor hopping amplitudes. The flow equation for the effective interaction is evaluated numerically on 1-loop level. The effective interactions diverge at a finite energy scale which is exponentially small for small bare interactions. To analyze the nature of the instabilities signalled by the diverging interactions we extend Salmhofers renormalization group for the calculation of susceptibilities. We compute the singlet superconducting susceptibilities for various pairing symmetries and also charge and spin density susceptibilities. Depending on the choice of the model parameters (hopping amplitudes, interaction strength and band-filling) we find commensurate and incommensurate antiferromagnetic instabilities or d-wave superconductivity as leading instability. We present the resulting phase diagram in the vicinity of half-filling and also results for the density dependence of the critical energy scale.