Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice

Abstract

We study the ground-state phase diagram of the frustrated quantum $J_1-J_2$ Heisenberg antiferromagnet on the honeycomb lattice using a mean field approach in terms of the Schwinger boson representation of the spin operators. We present results for the ground-state energy, local magnetization, energy gap and spin-spin correlations. The system shows magnetic long range order for $0\le J_2/J_1\lesssim 0.2075$ (Néel) and $0.398\lesssim J_2/J_1\le 0.5$ (spiral). In the intermediate region, we find two magnetically disordered phases: a gapped spin liquid phase which shows short-range Néel correlations $(0.2075\lesssim J_2/J_1\lesssim 0.3732)$, and a lattice nematic phase $(0.3732\lesssim J_2/J_1\lesssim 0.398)$, which is magnetically disordered but breaks lattice rotational symmetry. The errors in the values of the phase boundaries which are implicit in the number of significant figures quoted, correspond purely to the error in the extrapolation of our finite-size results to the thermodynamic limit.

11 pages, 9 figures, to appear in Phys. Rev. B

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