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-$1\mathrm{/}2$, we obtain $32$ $SU(2)$, $1808$ $U(1)$ and $384$ ${\mathbb{Z}}_2$ 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 ${\mathbb{Z}}_2$, distinct phases. We discuss their ground state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.