Multipolar ordering in the three-orbital Hubbard model

TL;DR

This paper investigates the ground-state phases of the three-orbital t2g Hubbard model, deriving multipolar order parameters and mapping phase diagrams to reveal complex quantum phases influenced by Coulomb interaction, spin-orbit coupling, and electron count.

Contribution

It introduces a comprehensive set of multipolar order parameters for t2g models and maps the phase diagrams using Hartree-Fock, highlighting novel quantum phases.

Findings

Identification of various nontrivial multipole orders.

Mapping of phase diagrams in Coulomb, SOC, and electron number space.

Discussion of future methods like dynamical mean-field theory.

Abstract

The ground-state phase diagrams of the three-orbital t2g Hubbard model are studied using a Hartree-Fock approximation. First, a complete set of multipolar order parameters for t2g models defined in terms of the effective total angular momentum jeff are theoretically derived. These order parameters can classify off-diagonal orders between jeff = 1/2 and jeff = 3/2 manifolds. Second, through extensive Hartree-Fock calculations, the ground-state phase diagrams in the space of (1) the onsite Coulomb repulsion U, (2) the spin-orbit coupling (SOC), and (3) the number of electrons are mapped out. A variety of nontrivial quantum phases with jeff-diagonal and jeff-off-diagonal multipole orders are found. Finally, future studies using more numerically expensive methods, such as dynamical mean-field theory are discussed.