Artificial $SU(3)$ Spin-Orbit Coupling and Exotic Mott Insulators

TL;DR

This paper develops an $SU(3)$ dynamical mean-field theory to explore how spin-orbit coupling influences Mott insulators in ultracold atomic systems, revealing complex magnetic phases and transitions.

Contribution

It introduces an unbiased $SU(N)$ real-space DMFT method to analyze the effects of spin-orbit coupling and interactions in $SU(3)$ systems, uncovering new magnetic phases.

Findings

Spin-orbit coupling stabilizes ferromagnetic, spiral, and stripe orders.

Phase diagram mapped in the large-$U$ limit.

Behavior of local observables across the metal-insulator transition.

Abstract

Motivated by recent progress in the realization of artificial gauge fields and $SU(N)$ Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased $SU(N)$ real-space dynamical mean-field theory (DMFT) approach to study the effect of spin-orbit coupling and onsite Hubbard interaction $U$ on $SU(3)$ fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large-$U$ limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnet, spiral, and stripes with different orientations in $SU(3)$ Mott insulators.