Projective symmetry group classification of Abrikosov fermion mean-field ans\"atze on the square-octagon lattice

TL;DR

This paper classifies symmetric quantum spin liquids on the square-octagon lattice using projective symmetry groups, identifying numerous phases with different gauge groups and analyzing their properties.

Contribution

It provides a comprehensive PSG classification for various gauge groups on the square-octagon lattice, including explicit enumeration of phases and their properties.

Findings

Identified 4 SU(2), 24 U(1), and 36 Z2 symmetric phases.

Analyzed ground state properties and spinon dispersions.

Reduced the classification to a manageable set of phases with short-range amplitudes.

Abstract

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-$1/2$, we obtain $32$ $SU(2)$, $1808$ $U(1)$ and $384$ $\mathbb{Z}_{2}$ algebraic PSGs. Constraining ourselves to mean-field parton ans\"atze 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.