Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids

Abstract

While the enhancement of the spin-space symmetry from the usual $\mathrm{SU}(2)$ to $\mathrm{SU}(N)$ is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here we propose a new mechanism by which the $\mathrm{SU}(4)$ symmetry emerges in the strong spin-orbit coupling limit. In $d^1$ transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently $\mathrm{SU}(4)$-breaking hopping between the $J_{\text{eff}}=3/2$ quartets. However, in the honeycomb structure, a gauge transformation maps the system to an $\mathrm{SU}(4)$-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in $\alpha$-ZrCl${}_3,$ the low-energy effective model is the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent $\mathrm{SU}(4)$ symmetry and space group symmetries.

6+7 pages, 3+2 figures, 1+1 tables

References in corpus (16)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Strong electronic correlations from Hund's coupling
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Spin-orbital quantum liquid on the honeycomb lattice
• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Weyl spin liquids
• Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model
• A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model
• Crystalline Kitaev spin liquids
• Exploring the spin-orbital ground state of Ba3CuSb2O9
• Dimer phases in quantum antiferromagnets with orbital degeneracy
• Resonating Valence-Bond State in an Orbitally Degenerate Quantum Magnet with Dynamical Jahn-Teller Effect

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