SU(6) Symmetry in a Model of Lattice Electrons: The Case of NaTiSi₂O₆

Dimerization of Ti³⁺ ions in NaTiSi₂O₆, a quasi-one-dimensional Mott insulator, has attracted considerable attention due to its possibility as a rare inorganic spin-Peierls material. Recently based on two-orbital models, it was suggested that this material has an orbital-assisted Peierls ground state [1]. Here we point out that in an ideal case, a remarkable property of NaTiSi₂O₆ is that its electronic band is exactly 3 times degenerate—with the lattice period of six Ti ions along the chain structure—despite the crystal field splitting of the three t2g orbitals into a local doublet and a higher energy singlet. We thus study NaTiSi₂O₆ in proximity to this case using density-functional theory and the SU(6)-symmetric Sutherland Hamiltonian. The perturbation from electron-lattice interactions breaks the SU(6) symmetry, leading to a spontaneous dimerization accompanied by a structural distortion having the characteristic length of about six Ti-Ti bonds.
[1] H. J. Silverstein et al., Phys. Rev. B 90, 140402(R) (2014) and references therein.