Multiflavor Mott insulators in quantum materials and ultracold atoms

Abstract

Mott insulators with large and active (or multiflavor) local Hilbert spaces widely occur in quantum materials and ultracold atomic systems, and are dubbed "multiflavor Mott insulators". For these multiflavored Mott insulating materials, the spin-only description with the quadratic spin interactions is often insufficient to capture the major physical processes. In the situation with active orbitals, the Kugel-Khomskii superexchange model was then proposed. We briefly review this historical model and discuss the modern developments beyond the original spin-orbital context. These include and are not restricted to the $4d$/$5d$ transition metal compounds with the spin-orbit-entangled $J=3/2$ quadruplets, the rare-earth magnets with two weakly-separated crystal field doublets, breathing magnets and/or the cluster and molecular magnets, et al. We explain the microscopic origin of the emergent Kugel-Khomskii physics in each realization with some emphasis on the $J=3/2$ quadruplets, and refer the candidate multiflavor Mott insulators as "$J=3/2$ Mott insulators". For the ultracold atoms, we review the multiflavor Mott insulator realization with the ultracold alkaline and alkaline-earth atoms on the optical lattices. Despite a large local Hilbert space from the atomic hyperfine spin states, the system could naturally realize a large symmetry group such as the Sp($N$) and SU($N$) symmetries. These ultracold atomic systems lie in the large-$N$ regime of these symmetry groups and are characterized by strong quantum fluctuations. The Kugel-Khomskii physics and the exotic quantum ground states with the "baryon-like" physics can appear in various limits. We conclude with our vision and outlook on this subject.

23 pages, 9 figures. To appear in NPJ Quantum materials

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• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
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• Dynamic Jahn-Teller Phenomena in Heavy Transition Metal Compounds
• SU($N$) symmetry with ultracold alkali dimers: weak dependence of scattering properties on hyperfine state
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• Zero Field Antiferromagnetically Coupled Skyrmions and their Field-Driven Uncoupling in Composite Chiral Multilayers
• Theory of Photocurrent and High-Harmonic Generation with Chiral Fermions
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• Gyrotropic magnetic effect in metallic chiral magnets
• First-principles studies of fermiology in topological phases of bulk ZrTe${}_5$