Weak ferromagnetism and other instabilities of the two-dimensional t-t' Hubbard model at Van Hove fillings

TL;DR

This study explores magnetic and superconducting phases in the 2D t-t' Hubbard model at Van Hove fillings, revealing a transition from spin-density waves to superconductivity and potential ferromagnetism influenced by next-nearest-neighbor hopping.

Contribution

It provides a detailed analysis of how varying t' affects magnetic and superconducting instabilities, highlighting the role of Kanamori screening and self-energy effects in these transitions.

Findings

Incommensurate spin-density wave emerges as |t'| increases from zero.

d_{x2-y2}-wave superconductivity dominates at intermediate |t'|.

Signs of ferromagnetism appear at large |t'| and low temperatures.

Abstract

We investigate magnetic and superconducting instabilities of the two-dimensional t-t' Hubbard model on a square lattice at Van Hove densities from weak to intermediate coupling by means of the two-particle self-consistent approach. We find that as the next-nearest-neighbor hopping |t'| increases from zero, the leading instability is towards an incommensurate spin-density wave whose wave vector moves slowly away from (pi, pi). For intermediate values of |t'|, the leading instability is towards d_{x2-y2}-wave superconductivity. For larger |t'|>0.33t, there are signs of a crossover to ferromagnetism at extremely low temperatures. The suppression of the crossover temperature is driven by Kanamori screening that strongly renormalizes the effective interaction and also causes the crossover temperature to depend only weakly on t'. Electronic self-energy effects for large |t'| lead to considerable reduction of single-particle spectral weight at zero energy at temperatures as high as T<0.1t, an effect that may be detrimental to the existence of a ferromagnetic ground state at weak coupling.