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 (J1β=1) and frustrating second-neighbor (J2β>0)
interactions. For the intermediate frustration regime 0.22β²J2ββ²0.36, we find a surprising antiferromagnetic Ising phase, with
ordered moments pointing along the z axis, despite the absence of any S_z_z
interactions in the Hamiltonian. Surrounding this phase as a function of J2β
are antiferromagnetic phases with the moments pointing in the xβy plane for
small J2β and a close competition between an xβy plane magnetic collinear
phase and a dimer phase for large values of J2β. We do not find any spin
liquid phases in this model.Comment: 5 pages, 5 figures, minor changes made for publication on PR