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APS

Frustrated bilayer spin one XY model on the honeycomb lattice

Antonio S. T. Pires

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

Abstract The spin-one honeycomb bilayer XY antiferromagnet has been studied taking into account the effect of the next-near neighbor J2 exchange interactions and single-ion easy plane anisotropy, using a flavor wave theory. We found that, at a critical point α C = 13.8 , where α = J ⊥ / J 1 is the ratio between the interlayer J ⊥ to the intralayer near neighbor J1 exchange interaction, the system shows a quantum phase transition from an Neel ordered phase to a paramagnetic phase. The phase diagram at zero temperature is presented.

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Frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin- 12 J1−J2−J1⊥ model

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We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-$\frac{1}{2}{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{\perp}}$ model on the honeycomb bilayer lattice. In each layer, we include both nearest-neighbor and frustrating next-nearest-neighbor antiferromagnetic exchange couplings, of strength ${J}_{1}>0$ and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant ${J}_{1}^{\ensuremath{\perp}}\ensuremath{\equiv}\ensuremath{\delta}{J}_{1}>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the N\'eel magnetic order parameter, as well as the triplet spin gap. By implementing the method to very high orders of approximation we obtain an accurate estimate for the full boundary of the N\'eel phase in the $\ensuremath{\kappa}\ensuremath{\delta}$ plane. For each value $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(0)\ensuremath{\approx}1.70(5)$, we find an upper critical value ${\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$, such that N\'eel order is present for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$. Conversely, for each value $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(0)\ensuremath{\approx}0.19(1)$, we find an upper critical value ${\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, such that N\'eel order persists for $0<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$. Most interestingly, for values of $\ensuremath{\kappa}$ in the range ${\ensuremath{\kappa}}_{c}(0)<\ensuremath{\kappa}<{\ensuremath{\kappa}}^{>}\ensuremath{\approx}0.215(2)$, we find a reentrant behavior such that N\'eel order exists only in the range ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, with ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})>0$. These latter upper and lower critical values coalesce when $\ensuremath{\kappa}={\ensuremath{\kappa}}^{>}$, such that ${\ensuremath{\delta}}_{c}^{<}({\ensuremath{\kappa}}^{>})={\ensuremath{\delta}}_{c}^{>}({\ensuremath{\kappa}}^{>})\ensuremath{\approx}0.25(5)$.

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We study the zero-temperature ($T=0$) ground-state (GS) properties of a frustrated spin-half ${J}_{1}^{\mathit{X}XZ}$--${J}_{2}^{\mathit{X}XZ}$ model on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings ${J}_{1}>0$ and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively, using the coupled cluster method. Both interactions are of the anisotropic XXZ type. We present the $T=0$ GS phase diagram of the model in the ranges $0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1$ of the spin-space anisotropy parameter and $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}1$ of the frustration parameter. A possible quantum spin-liquid region is identified.

arXiv:1404.0194•Physical Review B•Jun 24, 2014•24 citations
Abstract The spin-one honeycomb bilayer XY antiferromagnet has been studied taking into account the effect of the next-near neighbor J2 exchange interactions and single-ion easy plane anisotropy, using a flavor wave theory. We found that, at a critical point α C = 13.8 , where α = J ⊥ / J 1 is the ratio between the interlayer J ⊥ to the intralayer near neighbor J1 exchange interaction, the system shows a quantum phase transition from an Neel ordered phase to a paramagnetic phase. The phase diagram at zero temperature is presented.
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→∞.
Using the density matrix renormalization group on wide cylinders, we study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with first-neighbor (J1=1) and frustrating second-neighbor (J2>0) interactions. For the intermediate frustration regime 0.22≲J2≲0.36, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any S(z)S(z) interactions in the Hamiltonian. Surrounding this phase as a function of J2 are antiferromagnetic phases with the moments pointing in the x-y plane for small J2 and a close competition between an x-y plane magnetic collinear phase and a dimer phase for large values of J2. We do not find any spin-liquid phases in this model.
We study the nearest-neighbor exchange (J1{J}_{1}J1​) and second-nearest-neighbor exchange (J2{J}_{2}J2​) XYXYXY antiferromagnet on the honeycomb lattice using ground state series expansions around N\'eel, columnar, and dimer phases. The conventional two-sublattice XYXYXY N\'eel order at small J2{J}_{2}J2​ 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 XYXYXY and Ising degrees of freedom, namely the nearest-neighbor Ising and XYXYXY spin correlations become nearly equal. This suggests that the system is close to a bicritical point separating XYXYXY and Ising orders. At still larger J2/J1{J}_{2}/{J}_{1}J2​/J1​ the columnar and dimer energies are found to be nearly degenerate. At even larger J2{J}_{2}J2​ 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.
We use the coupled cluster method (CCM) to study a frustrated spin-12J1−J2−J1⊥ Heisenberg antiferromagnet on a bilayer honeycomb lattice with AA stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants J1 > 0 and J2 ≡ κJ1 > 0. The two layers are coupled with NN AFM exchanges with coupling strength J1⊥≡δJ1>0. We calculate to high orders of approximation within the CCM the zero-field transverse magnetic susceptibility χ in the Néel phase. We thus obtain an accurate estimate of the full boundary of the Néel phase in the κδ plane for the zero-temperature quantum phase diagram. We demonstrate explicitly that the phase boundary derived from χ is fully consistent with that obtained from the vanishing of the Néel magnetic order parameter. We thus conclude that at all points along the Néel phase boundary quasiclassical magnetic order gives way to a nonclassical paramagnetic phase with a nonzero energy gap. The Néel phase boundary exhibits a marked reentrant behavior, which we discuss in detail.
We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-$\frac{1}{2}{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{\perp}}$ model on the honeycomb bilayer lattice. In each layer, we include both nearest-neighbor and frustrating next-nearest-neighbor antiferromagnetic exchange couplings, of strength J1>0{J}_{1}>0J1​>0 and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant ${J}_{1}^{\ensuremath{\perp}}\ensuremath{\equiv}\ensuremath{\delta}{J}_{1}>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the N\'eel magnetic order parameter, as well as the triplet spin gap. By implementing the method to very high orders of approximation we obtain an accurate estimate for the full boundary of the N\'eel phase in the $\ensuremath{\kappa}\ensuremath{\delta}$ plane. For each value $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(0)\ensuremath{\approx}1.70(5)$, we find an upper critical value ${\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$, such that N\'eel order is present for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(\ensuremath{\delta})$. Conversely, for each value $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}(0)\ensuremath{\approx}0.19(1)$, we find an upper critical value ${\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, such that N\'eel order persists for $0<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$. Most interestingly, for values of $\ensuremath{\kappa}$ in the range ${\ensuremath{\kappa}}_{c}(0)<\ensuremath{\kappa}<{\ensuremath{\kappa}}^{>}\ensuremath{\approx}0.215(2)$, we find a reentrant behavior such that N\'eel order exists only in the range ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})<\ensuremath{\delta}<{\ensuremath{\delta}}_{c}^{>}(\ensuremath{\kappa})$, with ${\ensuremath{\delta}}_{c}^{<}(\ensuremath{\kappa})>0$. These latter upper and lower critical values coalesce when $\ensuremath{\kappa}={\ensuremath{\kappa}}^{>}$, such that ${\ensuremath{\delta}}_{c}^{<}({\ensuremath{\kappa}}^{>})={\ensuremath{\delta}}_{c}^{>}({\ensuremath{\kappa}}^{>})\ensuremath{\approx}0.25(5)$.
We study the zero-temperature (T=0T=0T=0) ground-state (GS) properties of a frustrated spin-half J1XXZ{J}_{1}^{\mathit{X}XZ}J1XXZ​--J2XXZ{J}_{2}^{\mathit{X}XZ}J2XXZ​ model on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings J1>0{J}_{1}>0J1​>0 and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively, using the coupled cluster method. Both interactions are of the anisotropic XXZ type. We present the T=0T=0T=0 GS phase diagram of the model in the ranges $0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1$ of the spin-space anisotropy parameter and $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}1$ of the frustration parameter. A possible quantum spin-liquid region is identified.