Unexpected z-direction Ising antiferromagnetic order in a frustrated spin-1/2 J 1-J 2 XY model on the honeycomb lattice

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 ($J_1 = 1$) and frustrating second-neighbor ($J_2>0$) interactions. For the intermediate frustration regime $0.22 < J_2 < 0.36$, 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 $J_2$ 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.