Classification of spin liquids on the stuffed honeycomb lattice

We introduce the stuffed honeycomb lattice (a honeycomb lattice coupled to its dual - a triangular lattice) that interpolates between the triangular and the honeycomb lattices. We consider S = 1/2 Heisenberg spins. Our classical phase diagram reveals a multi-critical point on the triangular lattice axis, with two new neighboring noncollinear phases appearing only off axis. Our quantum phase diagram found via exact diagonalization hosts a large spin liquid (SL) region that eats up most of the phase space of the new classical phases around the multi-critical point. We present a projective symmetry group analysis of all possible symmetric SLs on the stuffed honeycomb lattice and attempt to probe the possible nature (gapless, nematic, etc) to compare to the SL region found in exact diagonalization. Among these SLs, we focus on characterizing the competitive ones found in a variational Monte Carlo analysis.