Candidate quantum spin liquids on the maple-leaf lattice

Motivated by recent numerical studies reporting putative quantum paramagnetic behavior in spin-1/2 Heisenberg models on the maple-leaf lattice, we classify Abrikosov fermion mean-field Ans\"atze of fully symmetric U (1) and Z₂ quantum spin liquids within the framework of projective symmetry groups. We obtain a total of 17 U (1) and 12 Z₂ algebraic PSGs, and, upon restricting their realization via mean-field Ans\"atze with nearest-neighbor amplitudes (relevant to the studied models), only 12 U (1) and 8 Z₂ distinct phases are obtained. We present both singlet and triplet fields for all Ans\"atze up to third nearest-neighbor bonds and discuss their spinon dispersions as well as their dynamical spin structure factors. We further assess the effects of Gutzwiller projection on the equal-time spin structure factors, and identify a U (1) Fermi surface spin liquid whose structure factor most closely reproduces the one obtained from pseudo-fermion functional renormalization group calculations.