A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model

Abstract

We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ 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 $J_2\equiv \kappa J_1>0$, respectively. The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant $J_1^{\perp }\equiv \delta J_1>0$. We calculate directly in the infinite-lattice limit both the ground-state energy per spin and the Néel 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 Néel phase in the $\kappa \delta$ plane. For each value $\delta <{\delta }_c^{>}(0)\approx 1.70(5)$ we find an upper critical value ${\kappa }_c(\delta )$, such that Néel order is present for $\kappa <{\kappa }_c(\delta )$. Conversely, for each value $\kappa <{\kappa }_c(0)\approx 0.19(1)$ we find an upper critical value ${\delta }_c^{>}(\kappa )$, such that Néel order persists for $0<\delta <{\delta }_c^{>}(\kappa )$. Most interestingly, for values of $\kappa$ in the range ${\kappa }_c(0)<\kappa <{\kappa }^{>}\approx 0.215(2)$ we find a reentrant behavior such that Néel order exists only in the range ${\delta }_c^{<}(\kappa )<\delta <{\delta }_c^{>}(\kappa )$, with ${\delta }_c^{<}(\kappa )>0$. These latter upper and lower critical values coalesce when $\kappa ={\kappa }^{>}$, such that ${\delta }_c^{<}({\kappa }^{>})={\delta }_c^{>}({\kappa }^{>})\approx 0.25(5)$.

References in corpus (16)

• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Magnetic order on a frustrated spin-1/2 Heisenberg antiferromagnet on the Union Jack lattice
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Complete phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model (with $J_3=J_2$) on the honeycomb lattice
• High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
• Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice
• Quantum phase diagram of a frustrated antiferromagnet on the bilayer honeycomb lattice
• A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$
• Large-$s$ expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number $s$
• Self consistent study of the quantum phases in a frustrated antiferromagnet on the bilayer honeycomb lattice

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