An investigation of the quantum J ₁ - J ₂ - J ₃ model on the honeycomb lattice

Abstract:

We have investigated the quantum J ₁ - J ₂ - J ₃ model on the honeycomb lattice with exact diagonalizations and linear spin-wave calculations for selected values of J ₂ / J ₁ , J ₃ / J ₁ and antiferromagnetic (J ₁ > 0) or ferromagnetic (J ₁ < 0) nearest neighbor interactions. We found a variety of quantum effects: “order by disorder" selection of a Néel ordered ground-state, good candidates for non-classical ground-states with dimer long range order or spin-liquid like. The purely antiferromagnetic Heisenberg model is confirmed to be Néel ordered. Comparing these results with those observed on the square and triangular lattices, we enumerate some conjectures on the nature of the quantum phases in the isotropic models.