SU(4) materials: emergence and developments

Masahiko G. YAMADA

There is a lot of interest in finding and identifying novel quantum materials. We here focus on d^1 materials with a strong spin-orbit coupling, which are supposed to realize a much higher symmetry than SU(2), an emergent SU(4) symmetry [1,2].
In fact, alpha-ZrCl3 is expected to host the SU(4) Heisenberg model on the honeycomb lattice with a large frustration [3].
These "SU(4) materials" potentially realize a new type of spin liquids, a gapped Z4 spin liquid [4]. We present new density matrix renormalization group (DMRG) studies on the SU(4) Heisenberg model on the honeycomb lattice to show that the ground state is indeed gapped and symmetric with respect to all the symmetries, indicating the existence of a gapped spin liquid in this system [5].
The topological entanglement entropy is close to the expected value for the Z4 spin liquid, which has 16 superselection sectors in the thermodynamic limit.
Finally, we also indicate a relation to metal-organic frameworks or twisted bilayer graphene on this matter.

[1] M.G.Y., M. Oshikawa, and G. Jackeli, Phys. Rev. Lett. 121, 097201 (2018).
[2] M.G.Y., M. Oshikawa, and G. Jackeli, Phys. Rev. B 104, 224436 (2021).
[3] P. Corboz et al., Phys. Rev. X 2, 041013 (2012).
[4] M.G.Y., and S. Fujimoto, arXiv:2111.14470 (2021).
[5] M.G.Y., K. Penc, and F. Pollmann, to appear.