Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice

We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. Employing the Abrikosov fermion representation for spin 12, we obtain 32SU(2), 1808U(1), and 384Z2 algebraic PSGs. Constraining ourselves to mean-field parton ansätze with short-range amplitudes, the classification reduces to a limited number, with 4 SU(2), 24 U(1), and 36 Z2, distinct phases. We discuss their ground-state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.