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arXiv:1403.2252 · Physical Review B

Frustrated spin- 12 J1 – J2 isotropic XY model on the honeycomb lattice

R. F. Bishop, P. H. Y. Li, C. E. Campbell

Published Jun 17, 2014• 28 citations
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Abstract

We study the zero-temperature ground-state (GS) phase diagram of a spin-half ${J}_{1}$--${J}_{2}$ $XY$ model on the honeycomb lattice with nearest-neighbor exchange coupling ${J}_{1}>0$ and frustrating next-nearest-neighbor exchange coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, 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 $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}1$. In this range, we find phases exhibiting, respectively, N\'eel $xy$ planar [N(p)], N\'eel $z$-aligned [N($z$)], SDVBC, and N\'eel-II $xy$ planar [N-II(p)] orderings. The N\'eel-II states, which break the lattice rotational symmetry, are ones in which the spins of nearest-neighbor pairs along one of the three equivalent honeycomb directions are parallel, while those in the other two directions are antiparallel. The N(p) state, which is stable for the classical version of the model in the range $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}\frac{1}{6}$, is found to form the GS phase out to a first quantum critical point at ${\ensuremath{\kappa}}_{{c}_{1}}=0.216(5)$, beyond which the stable GS phase has N($z$) order over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}=0.355(5)$. For values $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}$, 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 ${\ensuremath{\kappa}}_{{c}_{2}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{3}}\ensuremath{\approx}0.52(3)$ is a mixed state with both SDVBC and N-II(p) forms of order; and for values $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{3}}$ is the N-II(p) state, which is stable at the classical level only at the highly degenerate point $\ensuremath{\kappa}=\frac{1}{2}$. Over the range $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}1$, we find no evidence for any of the spiral phases that are present classically for all values $\ensuremath{\kappa}>\frac{1}{6}$, nor for any quantum spin-liquid state.

DOI
10.1103/physrevb.89.214413

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Quantum phase diagram of a frustrated spin-12\frac{1}{2}21​ J1J_{1}J1​--J2J_{2}J2​--J1⊥J_{1}^{\perp}J1⊥​ Heisenberg model on an AAAAAA-stacked bilayer honeycomb lattice
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