Quantum disordered phase on the frustrated honeycomb lattice

Abstract

In the present paper we study the phase diagram of the Heisenberg model on the honeycomb lattice with antiferromagnetic interactions up to third neighbors along the line ${J}_{2}={J}_{3}$ that includes the point ${J}_{2}={J}_{3}={J}_{1}/2$, corresponding to the highly frustrated point where the classical ground state has macroscopic degeneracy. Using the linear spin-wave theory and the Schwinger boson technique followed by a mean field decoupling and exact diagonalization for small systems, we find an intermediate phase with a spin gap and short-range N\'eel correlations in the strong quantum limit $(S=\frac{1}{2})$. All techniques provide consistent results which allow us to predict the existence of a quantum disordered phase, which may have been observed in recent high-field ESR measurements in manganites.