We numerically study the SU(2) $\otimes$ SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially singular gap formation in consistent with the analytic approach, which is different from the previous numerical calculation. Furthermore, we find new critical phases around the SU(4) point, surrounding the previously known gapless symmetric line. In these novel phases either spin or orbital excitations around momentum $q=π$ form massless continua which split from the excitations belonging to the $[2^2]$ irreducible representation at the SU(4) point. On the critical symmetric line, the additional coupled spin-orbit excitations around $q=π/2$ originating from [ $2^11^2$ ] become critical, too.We numerically study the SU(2)$\otimes$SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially singular gap formation in consistent with the analytic approach, which is different from the previous numerical calculation. Furthermore, we find new critical phases around the SU(4) point, surrounding the previously known gapless symmetric line. In these novel phases either spin or orbital excitations around momentum $q=π$ form massless continua which split from the excitations belonging to the $[2^2]$ irreducible representation at the SU(4) point. On the critical symmetric line, the additional coupled spin-orbit excitations around $q=π/2$ originating from [$2^11^2$] become critical, too.

arXiv:cond-mat/9908237Journal of the Physical Society of JapanJan 1, 200049 citations

Spin Orbit Coupling in a Spin-1 System

Ryan Price, Daniel Campbell, Andika Putra +2 more

Bulletin of the American Physical SocietyJun 5, 20140 citations

Emergent SU ( 4 ) Symmetry in α − ZrCl 3 and Crystalline Spin-Orbital Liquids

Masahiko G. Yamada, Masaki Oshikawa, George Jackeli

While the enhancement of spin-space symmetry from the usual SU(2) to 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 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 SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the 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 SU(4) symmetry and space group symmetries.While the enhancement of spin-space symmetry from the usual SU(2) to 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 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 SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the 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 SU(4) symmetry and space group symmetries.

arXiv:1709.05252Physical Review LettersAug 27, 201888 citations

We numerically study the SU(2)

\otimes

SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially singular gap formation in consistent with the analytic approach, which is different from the previous numerical calculation. Furthermore, we find new critical phases around the SU(4) point, surrounding the previously known gapless symmetric line. In these novel phases either spin or orbital excitations around momentum

q=π

form massless continua which split from the excitations belonging to the

[2^2]

irreducible representation at the SU(4) point. On the critical symmetric line, the additional coupled spin-orbit excitations around

q=π/2

originating from [

2^11^2

] become critical, too.