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arXiv:1403.1905 · Physical Review B

Phase diagram of the frustrated quantum- XY model on the honeycomb lattice studied by series expansions: Evidence for proximity to a bicritical point

J. Oitmaa, Rajiv R. P. Singh

Published Mar 27, 2014• 6 citations
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Abstract

We study the nearest-neighbor exchange (${J}_{1}$) and second-nearest-neighbor exchange (${J}_{2}$) $XY$ antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice $XY$ N\'eel order at small ${J}_{2}$ vanishes at ${J}_{2}/{J}_{1}=0.22\ifmmode\pm\else\textpm\fi{}0.01$ in agreement with results from density matrix renormalization group (DMRG) studies. Near the transition, we find evidence for an approximate emergent symmetry between $XY$ and Ising degrees of freedom, namely the nearest-neighbor Ising and $XY$ spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating $XY$ and Ising orders. At still larger ${J}_{2}/{J}_{1}$ the columnar and dimer energies are found to be nearly degenerate. At even larger ${J}_{2}$ the columnar phase is obtained. The ground state energies in all three phases are in good agreement with the values found in the DMRG studies.

DOI
10.1103/physrevb.89.104423

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We study the zero-temperature ground-state (GS) phase diagram of a spin-half J1{J}_{1}J1​--J2{J}_{2}J2​ XYXYXY model on the honeycomb lattice with nearest-neighbor exchange coupling J1>0{J}_{1}>0J1​>0 and frustrating next-nearest-neighbor exchange coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, where both bonds are of the isotropic XYXYXY 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 xyxyxy planar [N(p)], N\'eel zzz-aligned [N(zzz)], SDVBC, and N\'eel-II xyxyxy 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(zzz) 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.
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