Ferromagnetism and orbital order in the two-orbital Hubbard model

TL;DR

This study explores the magnetic and orbital phases of the two-orbital Hubbard model on a square lattice at quarter-filling, revealing a ferromagnetic state with antiferro-orbital order in strong interactions and disordered states at weaker interactions.

Contribution

It provides a variational Monte Carlo analysis of the ground states, highlighting the dominance of ferromagnetic and antiferro-orbital order in strong Coulomb interactions.

Findings

Strong Coulomb interactions favor ferromagnetic and AF-orbital order.

Weaker interactions lead to disordered states.

Purely orbital ordered and partial ferromagnetic states are not ground states.

Abstract

We investigate spin and orbital states of the two-orbital Hubbard model on a square lattice by using a variational Monte Carlo method at quarter-filling, i.e., the electron number per site is one. As a variational wave function, we consider a Gutzwiller projected wave function of a mean-field type wave function for a staggered spin and/or orbital ordered state. Then, we evaluate expectation value of energy for the variational wave functions by using the Monte Carlo method and determine the ground state. In the strong Coulomb interaction region, the ground state is the perfect ferromagnetic state with antiferro-orbital (AF-orbital) order. By decreasing the interaction, we find that the disordered state becomes the ground state. Although we have also considered the paramagnetic state with AF-orbital order, i.e., purely orbital ordered state, and partial ferromagnetic states with and without AF-orbital order, they do not become the ground state.