Quantum phases of the frustrated XY models on the honeycomb lattice

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Searching for spin liquid states has long been attracting both experimentalists and theorists. In this article, we review recent density matrix renormalization group studies 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, there exists a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any Sz Sz 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. No spin-liquid phases was found in the XY model even with the third neighbor (J₃>0) interactions.