Publisher’s Note: Kaleidoscope of Exotic Quantum Phases in a FrustratedXYModel [Phys. Rev. Lett.107, 077201 (2011)]

Nature of the phases in the frustratedXYmodel on the honeycomb lattice

“…There, evidence was found supporting the existence of a spin liquid surrounded by two magnetically ordered states, namely, an antiferromagnetic (collinear) state at lower (higher) J 2 /J 1 . The spin-liquid phase was suggested to be gapless and characterized by a distinctive parameter dependent feature in the momentum distribution n(k), similar to a Bose surface, thus suggesting the presence of an exotic Bose metal [20,24,[26][27][28][29][30][31].…”

“…Another model that has recently received considerable attention for its potential to realize spin-liquid states is the spin-1/2 Heisenberg model on the honeycomb lattice, with nearest-neighbor (NN) J 1 and next-to-nearest neighbor (NNN) J 2 exchange interactions [7][8][9][10][11][12][13][14][15][16]. This is in part motivated by its close relation to the Hubbard model, for which the possibility of having a spin-liquid ground state has been under close scrutiny [17][18][19].A closely related spin model with a rich phase diagram and the promise to support a gapless spin liquid phase is the J 1 − J 2 spin-1/2 XY model on the honeycomb lattice [20,21], which is the main subject of this Rapid Communication. Its Hamiltonian can be written as…”

“…A closely related spin model with a rich phase diagram and the promise to support a gapless spin liquid phase is the J 1 − J 2 spin-1/2 XY model on the honeycomb lattice [20,21], which is the main subject of this Rapid Communication. Its Hamiltonian can be written as…”

“…This model can be thought of as a Haldane-Bose-Hubbard model [20,[22][23][24], i.e., the Haldane model [25] on the honeycomb lattice with NN hopping J 1 and complex NNN hopping |J 2 |e ıφ , where spinless fermions are replaced by hard-core bosons and φ = 0. Hard-core boson creation and annihilation operators can then be mapped onto spin operators (…”

“…[20] by means of exact diagonalization on small clusters. There, evidence was found supporting the existence of a spin liquid surrounded by two magnetically ordered states, namely, an antiferromagnetic (collinear) state at lower (higher) J 2 /J 1 .…”