Designer Spin Models in Tunable Two-Dimensional Nanographene Lattices

Motivated by recent experimental breakthroughs, we propose a strategy for designing two-dimensional spin-lattices with competing interactions that lead to nontrivial emergent quantum states. We consider S = ¹/₂ nanographenes with C₃ symmetry as building blocks, and we leverage the potential to control both the sign and the strength of exchange with first neighbors to build a family of spin models. Specifically, we consider the case of a Heisenberg model in a triangle-decorated honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions whose ratio can be varied in a wide range. On the basis of the exact diagonalization of both Fermionic and spin models, we predict a quantum phase transition between a valence bond crystal of spin singlets with triplon excitations living in a Kagomé lattice and a Néel phase of effective S = ³/₂ in the limit of dominant ferromagnetic interactions.