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

TL;DR

This paper proposes a mechanism for emergent SU(4) symmetry in certain transition metal compounds with strong spin-orbit coupling, leading to potential gapless spin-orbital liquids in honeycomb and 3D lattice structures.

Contribution

It introduces a new way for SU(4) symmetry to emerge in materials with strong spin-orbit coupling, enabling the realization of spin-orbital liquids.

Findings

In $ ext{α-ZrCl}_3$, the low-energy model is an SU(4) Heisenberg model.

The emergent SU(4) symmetry is protected by space group symmetries.

Predicted gapless spin-orbital liquids in honeycomb and 3D lattices.

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 $J_\textrm{eff}=3/2$ 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.