The frustrated spin-1/2 J₁--J₂ isotropic XY model on the honeycomb lattice

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We study the zero-temperature ground-state (GS) phase diagram of a spin-half J₁--J₂ XY model on the honeycomb lattice with nearest-neighbor exchange coupling J₁>0 and frustrating next-nearest-neighbor exchange coupling J₂ ≡ κJ₁>0, where both bonds are of the isotropic XY type, using the coupled cluster method. Results are presented for the GS energy per spin, magnetic order parameter, and staggered dimer valence-bond crystalline (SDVBC) susceptibility, for values of the frustration parameter in the range 0 ≤ κ≤ 1. In this range we find phases exhibiting, respectively, Néel xy planar [N(p)], Néel z-aligned [N(z)], SDVBC, and Néel-II xy planar [N-II(p)] orderings which break the lattice rotational symmetry. The N(p) state, which is stable for the classical version of the model in the range 0 ≤ κ≤ 1/6, is found to form the GS phase out to a first quantum critical point at κc₁ = 0.216(5), beyond which the stable GS phase has N(z) order over the range κc₁ < κ< κc₂=0.355(5). For values κ> κc₂ we find a strong competition to form the GS phase between states with N-II(p) and SDVBC forms of order. Our best estimate, however, is that the stable GS phase over the range κc₂ < κ< κc₃ ≈ 0.52(3) is a mixed state with both SDVBC and N-II(p) forms of order; and for values κ> κc₃ is the N-II(p) state, which is stable at the classical level only at the highly degenerate point κ=1/2. Over the range 0 ≤ κ≤ 1 we find no evidence for any of the spiral phases that are present classically for all values κ> 1/6, nor for any quantum spin-liquid state.