Symmetry Classes of Spin and Orbital Ordered States in a t_{2g} Hubbard Model on a Two-dimensional Square Lattice

TL;DR

This paper classifies symmetry-broken spin and orbital ordered states in a two-dimensional t_{2g} Hubbard model using group theory, revealing various non-collinear magnetic states as potential ground states.

Contribution

It introduces a group theoretical bifurcation approach to systematically identify symmetry classes of Hartree-Fock solutions in a 2D Hubbard model, including novel non-collinear magnetic orbital states.

Findings

Multiple symmetry-broken solutions bifurcate from the normal state.

Non-collinear magnetic orbital ordered states can be ground states.

Numerical results support the stability of these states for certain parameters.

Abstract

This paper presents symmetry classes of the Hartree-Fock (HF) solutions of spin and orbital ordered states in a t_{2g} Hubbard model on a two-dimensional square lattice. Using a group theoretical bifurcation theory of the Hartree Fock equation, we obtained many types of broken symmetry solutions which bifurcate from the normal state through one step transition in cases of commensurate ordering vectors Q_0=(0,0), Q_1=(\pi,\pi), Q_2=(\pi,0) and Q_3=(0,\pi). Each broken symmetry state is characterized by the presence of local order parameters(LOP) at each lattice site: quadrupole moment Q=(Q_2^2,Q_{12},Q_{23},Q_{31}), orbital angular momentum l=(l_1,l_2,l_3), spin density s=(s^1,s^2,s^3), spin quadrupole moment Q^{\lambda}=(Q_2^{2\lambda}, Q_{12}^{\lambda},Q_{23}^{\lambda},Q_{31}^{\lambda}) and spin orbital angular momentum l^{\lambda}=(l_1^{\lambda},l_2^{\lambda},l_3^{\lambda}) where \lambda=1,2,3. We performed numerical calculations for some parameter sets. Then we have found that many types of non-collinear magnetic orbital ordered states having LOP:Q^{\lambda} and l^{\lambda} can be the ground state for these parameter sets.