Magnetic order and paramagnetic phases in the quantum J₁-J ₂-J₃ honeycomb model

Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J₁, J₂, and J₃ up to third nearest neighbors. We use an unbiased pseudofermion functional renormalization-group method to compute the magnetic susceptibility and to determine the ordered and disordered states of the model. Aside from antiferromagnetic-, collinear-, and spiral-order domains, we find a large paramagnetic region at intermediate J₂ coupling. For larger J₂ within this domain, we find a strong tendency for staggered dimer ordering, while the remaining paramagnetic regime for low J₂ shows only weak plaquette and staggered dimer responses. We suggest this regime to be a promising region for looking for quantum spin-liquid states when charge fluctuations would be included.