Unexpected z-direction ising antiferromagnetic order in a frustrated spin-1/2 J₁-J₂ XY model on the honeycomb lattice

Using the density matrix renormalization group 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 (J ₂>0) interactions. For the intermediate frustration regime 0.22 J₂ 0.36, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any S _zS_z 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.