Ferromagnetism in the two dimensional t-t' Hubbard model at the Van Hove density

TL;DR

This study investigates ferromagnetism in the two-dimensional t-t' Hubbard model at Van Hove filling using advanced quantum Monte Carlo simulations, revealing ferromagnetic and antiferromagnetic phases depending on hopping parameters.

Contribution

It introduces an improved projection quantum Monte Carlo method to analyze magnetic phases in the Hubbard model at Van Hove density.

Findings

Ferromagnetism observed at R=0.94

Antiferromagnetism observed at R=0.2

Results align with T-matrix approximation predictions

Abstract

Using an improved version of the projection quantum Monte Carlo technique, we study the square-lattice Hubbard model with nearest-neighbor hopping t and next-nearest-neighbor hopping t', by simulation of lattices with up to 20 X 20 sites. For a given R=2t'/t, we consider that filling which leads to a singular density of states of the noninteracting problem. For repulsive interactions, we find an itinerant ferromagnet (antiferromagnet) for R=0.94 (R=0.2). This is consistent with the prediction of the T-matrix approximation, which sums the most singular set of diagrams.