Flow to strong coupling in the two-dimensional Hubbard model

TL;DR

This paper uses a temperature flow formalism to analyze the renormalization group flow in the 2D Hubbard model near half-filling, revealing conditions under which various susceptibilities diverge, indicating complex strongly coupled phases.

Contribution

It extends the renormalization group analysis of the 2D Hubbard model using a novel temperature flow approach, exploring the interplay of competing orders near half-filling.

Findings

d-wave pairing susceptibility diverges when Fermi surface is inside the Umklapp surface

Multiple susceptibilities grow together near saddle points, indicating strong coupling

Indications of a non-trivial phase with short-range superconducting and antiferromagnetic correlations

Abstract

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t=-0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder.