Abstract
An emergent $\mathrm{SU}(4)$ symmetry discovered in the microscopic model for $d^1$ honeycomb materials [M.~G.~Yamada, M.~Oshikawa, and G.~Jackeli, Phys. Rev. Lett. \textbf{121}, 097201 (2018).] has enabled us to tailor exotic $\mathrm{SU}(4)$ models in real materials. In the honeycomb structure, the emergent $\mathrm{SU}(4)$ Heisenberg model would potentially have a quantum spin-orbital liquid ground state due to the \textit{multicomponent frustration}, and we can expect similar spin-orbital liquids also in three-dimensinal versions of the honeycomb lattice. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and entangled together due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic \textit{orbitalon} excitations at low temperature.
Highlights
The material realization of an SU(N ) symmetry with N > 2 was a long-standing problem
We note that the phase factor ηij cancels out in this second-order perturbation. This SU[4] Heisenberg model on the honeycomb lattice is established to host a gapless QSOL4, so we have found a possible realization of a Dirac spinorbital liquid in α-ZrCl3 with an emergent SU[4] symmetry
We made a comprehensive study on various d1 spin-orbit coupled systems and discovered that the SU[4] Heisenberg models appear generically on many tricoordinated bipartite lattices
Summary
The material realization of an SU(N ) symmetry with N > 2 was a long-standing problem. The potential of an emergent SU[4] symmetry in spin-orbital d1 honeycomb materials has stimulated research on various SU[4] models from two to three dimensions, including a prediction of a spinon-orbitalon Fermi surface in the threedimensional (3D) case. In these d1 materials with one electron in a d-shell, the low-energy effective spin-orbital model becomes the SU[4] Heisenberg model, which had been previously very difficult to be realized even in cold atomic systems. We first introduce a notion of an emergent SU[4] symmetry in spin-orbital systems (Sec. II), derive it in the most general form, and discuss the possibility of various QSOLs in the material realization of the SU[4] Heisenberg models (Sec. III).
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