Variational Monte Carlo study of ferromagnetism in the two-orbital Hubbard model on a square lattice

TL;DR

This study uses variational Monte Carlo methods to explore how orbital degeneracy and Hund's rule coupling influence ferromagnetism in the two-orbital Hubbard model on a square lattice, revealing multiple ferromagnetic phases.

Contribution

It introduces a variational Monte Carlo approach to identify and characterize ferromagnetic phases driven by orbital degeneracy and Hund's coupling in the two-orbital Hubbard model.

Findings

Ferromagnetic phase with orbital order at quarter-filling.

Antiferromagnetic phase without orbital order at half-filling.

Wide region of ferromagnetism for large Hund's coupling.

Abstract

To understand effects of orbital degeneracy on magnetism, in particular effects of Hund's rule coupling, we study the two-orbital Hubbard model on a square lattice by a variational Monte Carlo method. As a variational wave function, we consider a Gutzwiller projected wave function for a staggered spin and/or orbital ordered state. We find a ferromagnetic phase with staggered orbital order around quarter-filling, i.e., electron number n=1 per site, and an antiferromagnetic phase without orbital order around half-filling n=2. In addition, we find that another ferromagnetic phase without orbital order realizes in a wide filling region for large Hund's rule coupling. These two ferromagnetic states are metallic except for quarter filling. We show that orbital degeneracy and strong correlation effects stabilize the ferromagnetic states.