Unconventional orders in the maple-leaf ferro-antiferromagnetic Heisenberg model

Abstract Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-1/2 Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons J h and ferromagnetic couplings on triangles J t and dimer J d bonds is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around J d = J t = 0, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c120° antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases, which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger–Tisza treatment of the model providing insights from the semi-classical limit.