Frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-1/2 J1-J2-J1⊥ model

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