Frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-½ <i>J</i>₁- <i>J</i>₂-<i>J</i>₁^⊥ model

We use the coupled cluster method to study the zero-temperature quantum phase diagram of the spin-½ J1-J2-J1⊥ 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 &gt; 0 and J2 ≡ κJ1 &gt; 0, respectively.  The two layers are coupled by an interlayer nearest-neighbor exchange, with coupling constant J1⊥≡ δJ1 &gt; 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 κδ plane.  For each value δ &lt; δc&gt; (0) ≈1.70(5), we find an upper critical value κc(δ), such that Néel order is present for κ &lt; κc(δ).  Conversely, for each value κ &lt; κc (0) ≈ 0.19(1), we find an upper critical value δc&gt;(κ), such that Néel order persists for 0 &lt; δ &lt; δc&gt;(κ).  Most interestingly, for values of κ in the range κc(0) &lt; κ &lt; κ&gt; ≈ 0.215(2), we find a reentrant behavior such that Néel order exists only in the range δc&lt;(κ) &lt; δ &lt; δc&gt;(κ), with δc&lt;(κ) &gt; 0.  These latter upper and lower critical values coalesce when κ = κ&gt;, such that δc&lt;(κ&gt;) = δc&gt; (κ&gt;) ≈ 0.25(5)

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half {\it XXZ} antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart

Gapped paramagnetic state in a frustrated spin-½ Heisenberg antiferromagnet on the cross-striped square lattice

We implement the coupled cluster method to very high orders of approximation to study the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ Heisenberg model on a cross-striped square lattice. Every nearest-neighbour pair of sites on the square lattice has an isotropic antiferromagnetic exchange bond of strength $J_{1}>0$, while the basic square plaquettes in alternate columns have either both or neither next-nearest-neighbour (diagonal) pairs of sites connected by an equivalent frustrating bond of strength $J_{2} \equiv \alpha J_{1} > 0$. By studying the magnetic order parameter (i.e., the average local on-site magnetization) in the range $0 \leq \alpha \leq 1$ of the frustration parameter we find that the quasiclassical antiferromagnetic N\'{e}el and (so-called) double N\'{e}el states form the stable ground-state phases in the respective regions $\alpha \alpha_{1b}^{c} = 0.615(5)$. The double N\'{e}el state has N\'{e}el ($\cdots\uparrow\downarrow\uparrow\downarrow\cdots$) ordering along the (column) direction parallel to the stripes of squares with both or no $J_{2}$ bonds, and spins alternating in a pairwise ($\cdots\uparrow\uparrow\downarrow\downarrow\uparrow\uparrow\downarrow\downarrow\cdots$) fashion along the perpendicular (row) direction, so that the parallel pairs occur on squares with both $J_{2}$ bonds present. Further explicit calculations of both the triplet spin gap and the zero-field uniform transverse magnetic susceptibility provide compelling evidence that the ground-state phase over all or most of the intermediate regime $\alpha_{1a}^{c} < \alpha < \alpha_{1b}^{c}$ is a gapped state with no discernible long-range magnetic order