A chiral SU(3) network model on the honeycomb lattice: an analytical construction of emergent SU(3)1 topological order

In this analytical mean-field study we construct and analyze a chiral SU(3) spin model on the bi- partite honeycomb lattice. Assigning the fundamental and antifundamental representations of SU(3) to the two sublattices, as required to form a singlet on every bond, together with the choice N = 3, fixes the on-site degree of freedom to a qutrit and the two-site coupling to the SU(3) Heisenberg exchange. By a standard representation-theoretic argument, the single-site reduced entropy equals ln 3 exactly in any finite-size singlet ground state. We show that the natural make-before-break ring exchange around a hexagonal plaquette must advance the site states by two positions to respect the alternation of conjugate representations, and that its time-reversal-odd part decomposes exactly into SU(3) scalar chiralities on the two sublattice triangles of the hexagon, leaving a one-parameter model. A fermionic parton mean-field analysis, with a single U(1) gauge constraint, places the parton bands at the Heisenberg point in a topologically trivial gapped state and shows, through an explicit Wick decoupling of the six-site ring exchange, that the chiral term generates a competing Haldane flux; enforcing the constraint self-consistently, the gap inverts beyond a finite coupling into a phase in which each of the three color bands carries unit Chern number. Integrating out the partons yields an SU(3)1 chiral spin liquid. The candidate phase carries total quantum dimension√3, three anyon sectors with Z3 fusion, chiral central charge two, and topological entanglement entropy ln √3. We present the exact operator identities as an algebraic foundation, and the SU(3)1 identification as a mean-field prediction, for future high-performance tensor-network investigations, which we identify as the necessary test of the proposed phase.