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arXiv:1410.6003 · Physical Review B

Quasiclassical magnetic order and its loss in a spin- 1 2 Heisenberg antiferromagnet on a triangular lattice with competing bonds

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

Published Jan 22, 2015• 86 citations
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Abstract

We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-$\frac{1}{2}$ ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings ${J}_{1}>0$ and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively, in the window $0\ensuremath{\le}\ensuremath{\kappa}<1$. The classical version of the model has a single GS phase transition at ${\ensuremath{\kappa}}^{\mathrm{cl}}=\frac{1}{8}$ in this window from a phase with 3-sublattice antiferromagnetic (AFM) ${120}^{\ensuremath{\circ}}$ N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}^{\mathrm{cl}}$ to an infinitely degenerate family of 4-sublattice AFM N\'eel phases for $\ensuremath{\kappa}>{\ensuremath{\kappa}}^{\mathrm{cl}}$. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case $\ensuremath{\kappa}=0$ of the spin-$\frac{1}{2}$ model for the GS energy per spin, $E/N=\ensuremath{-}0.5521(2){J}_{1}$, and the GS magnetic order parameter, $M=0.198(5)$ (in units where the classical value is ${M}^{\mathrm{cl}}=\frac{1}{2}$), which are among the best available. For the spin-$\frac{1}{2}$ ${J}_{1}\ensuremath{-}{J}_{2}$ model we find that the classical transition at $\ensuremath{\kappa}={\ensuremath{\kappa}}^{\mathrm{cl}}$ is split into two quantum phase transitions at ${\ensuremath{\kappa}}_{1}^{c}=0.060(10)$ and ${\ensuremath{\kappa}}_{2}^{c}=0.165(5)$. The two quasiclassical AFM states (viz., the ${120}^{\ensuremath{\circ}}$ N\'eel state and the striped state) are found to be the stable GS phases in the regime $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{1}^{c}$ and $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{2}^{c}$, respectively, while in the intermediate regimes ${\ensuremath{\kappa}}_{1}^{c}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{2}^{c}$ the stable GS phase has no evident long-range magnetic order.

DOI
10.1103/physrevb.91.014426

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•May 3, 2018•0 citations
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We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor (J1)({J}_{1})(J1​) and next-nearest-neighbor (J2)({J}_{2})(J2​) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1{J}_{2}/{J}_{1}J2​/J1​ and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin SSS, for J2/J1<1/8{J}_{2}/{J}_{1}<1/8J2​/J1​<1/8, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for J2=0{J}_{2}=0J2​=0, and for 1/8<J2/J1<11/8<{J}_{2}/{J}_{1}<11/8<J2​/J1​<1, they select the canted stripe state for all nonzero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary SSS, including S=1/2S=1/2S=1/2, near the saturation field by exploring the fact that near saturation the density of bosons is small for all SSS. We show that for S>1S>1S>1, the transition remains first order, with a finite hysteresis width, but for S=1/2S=1/2S=1/2 and, possibly, S=1S=1S=1, there appears a new intermediate phase without a quasiclassical long-range order.
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
The zero-temperature quantum phase diagram of the spin-12\frac{1}{2}21​ J1J_{1}J1​--J2J_{2}J2​--J1⊥J_{1}^{\perp}J1⊥​ model on an AAAAAA-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths J1>0J_{1} > 0J1​>0 and J2≡κJ1>0J_{2} \equiv \kappa J_{1}>0J2​≡κJ1​>0. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength J1⊥≡δJ1J_{1}^{\perp} \equiv \delta J_{1}J1⊥​≡δJ1​. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases, are calculated in the κδ\kappa \deltaκδ half-plane with κ>0\kappa > 0κ>0. Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter MMM and the excitation energy Δ\DeltaΔ from the sTz=0s^{z}_{T}=0sTz​=0 ground state to the lowest-lying ∣sTz∣=1|s^{z}_{T}|=1∣sTz​∣=1 excited state (where sTzs^{z}_{T}sTz​ is the total zzz component of spin for the system as a whole, and where the collinear ordering lies along the zzz direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (n≤10n \leq 10n≤10) in a systematic series of approximations involving nnn-spin clusters. The sole approximation made is then to extrapolate the sequences of nnnth-order results for MMM and Δ\DeltaΔ to the exact limit, n→∞n \to \inftyn→∞.