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 (J(1) = 1) and frustrating second-neighbor (J(2) > 0) interactions. For the intermediate frustration regime 0.22 less than or similar to J(2) less than or similar to 0.36, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any SzSz interactions in the Hamiltonian. Surrounding this phase as a function of J(2) are antiferromagnetic phases with the moments pointing in the x - y plane for small J(2) and a close competition between an x - y plane magnetic collinear phase and a dimer phase for large values of J(2). We do not find any spin-liquid phases in this model.