Unexpected z-Direction Ising Antiferromagnetic Order in a frustrated Spin-1/2 J₁-J₂ XY Model on the Honeycomb Lattice

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Using the density matrix renormalization group (DMRG) on wide cylinders, we study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with first-neighbor (J₁ = 1) and frustrating second-neighbor (J₂>0) interactions. For the intermediate frustration regime 0.22 J₂0.36, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any Szz interactions in the Hamiltonian. Surrounding this phase as a function of J₂ are antiferromagnetic phases with the moments pointing in the x-y plane for small J₂ and a close competition between an x-y plane magnetic collinear phase and a dimer phase for large values of J₂. We do not find any spin liquid phases in this model.