Weak Coupling Phases of the Attractive $t-t'$ Hubbard Model at the Van Hove Filling

TL;DR

This paper uses a renormalization group approach to analyze the phase diagram of the attractive $t-t'$ Hubbard model at Van Hove filling, revealing competing superconducting and charge-density-wave phases with a complex phase boundary.

Contribution

It provides a detailed analysis of the weak coupling phases of the attractive $t-t'$ Hubbard model at Van Hove filling using a Wilsonian RG approach, highlighting the phase boundary and instabilities.

Findings

Identification of a large boundary between superconducting and charge-density-wave phases.

Existence of a triple point where phases merge and phase separation occurs.

Phase separation instability persists at very low coupling constants.

Abstract

We apply a wilsonian renormalization group approach to the continuum limit of the attractive $t-t'$ Hubbard model, taken when the Fermi level is at the Van Hove singularity of the density of states. The model has well-defined scaling properties and the effective couplings display an unbounded flow in the infrared. We determine the leading instabilities by computing the different response functions up to $t' = 0.5 t$. The phase diagram shows a large boundary between superconducting and charge-density-wave phases, that merge in a triple point with a phase separation instability. The latter is realized down to very low coupling constant, as the Fermi sea degenerates towards a pair of straight lines near $t' = 0.5 t$.