High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. N\'eel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the N\'eel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table

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)

A frustrated quantum spin-{\boldmath s} model on the Union Jack lattice with spins {\boldmath s>1/2}

The zero-temperature phase diagrams of a two-dimensional frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number $s=1$ and $s=3/2$. The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that all nearest-neighbour (NN) exchange bonds are present with identical strength $J_{1}>0$, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength $J_{2} \equiv \kappa J_{1} > 0$. The bonds are arranged such that on the $2 \times 2$ unit cell they form the pattern of the Union Jack flag. Clearly, the NN bonds by themselves (viz., with $J_{2}=0$) produce an antiferromagnetic N\'{e}el-ordered phase, but as the relative strength $\kappa$ of the frustrating NNN bonds is increased a phase transition occurs in the classical case ($s \rightarrow \infty$) at $\kappa^{\rm cl}_{c}=0.5$ to a canted ferrimagnetic phase. In the quantum cases considered here we also find strong evidence for a corresponding phase transition between a N\'{e}el-ordered phase and a quantum canted ferrimagnetic phase at a critical coupling $\kappa_{c_{1}}=0.580 \pm 0.015$ for $s=1$ and $\kappa_{c_{1}}=0.545 \pm 0.015$ for $s=3/2$. In both cases the ground-state energy $E$ and its first derivative $dE/d\kappa$ seem continuous, thus providing a typical scenario of a second-order phase transition at $\kappa=\kappa_{c_{1}}$, although the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition.Comment: 1

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure

Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets

Using the coupled cluster method we investigate spin-$s$ $J_{1}$-$J_{2}'$ Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, triangular lattice when the spin quantum number $s=1$ or $s=3/2$. With respect to a square-lattice geometry the model has antiferromagnetic ($J_{1} > 0$) bonds between nearest neighbours and competing ($J_{2}' > 0$) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same one in each square. In a topologically equivalent triangular-lattice geometry, we have two types of nearest-neighbour bonds: namely the $J_{2}' \equiv \kappa J_{1}$ bonds along parallel chains and the $J_{1}$ bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at $\kappa = 0$ and a set of decoupled chains at $\kappa \rightarrow \infty$, with the isotropic HAF on the triangular lattice in between at $\kappa = 1$. For both the $s=1$ and the $s=3/2$ models we find a second-order quantum phase transition at $\kappa_{c}=0.615 \pm 0.010$ and $\kappa_{c}=0.575 \pm 0.005$ respectively, between a N\'{e}el antiferromagnetic state and a helical state. In both cases the ground-state energy $E$ and its first derivative $dE/d\kappa$ are continuous at $\kappa=\kappa_{c}$, while the order parameter for the transition (viz., the average on-site magnetization) does not go to zero on either side of the transition. The transition at $\kappa = \kappa_{c}$ for both the $s=1$ and $s=3/2$ cases is analogous to that observed in our previous work for the $s=1/2$ case at a value $\kappa_{c}=0.80 \pm 0.01$. However, for the higher spin values the transition is of continuous (second-order) type, as in the classical case, whereas for the $s=1/2$ case it appears to be weakly first-order in nature (although a second-order transition could not be excluded).Comment: 17 pages, 8 figues (Figs. 2-7 have subfigs. (a)-(d)

A Coupled-Cluster Formulation of Hamiltonian Lattice Field Theory: The Non-Linear Sigma Model

We apply the coupled cluster method (CCM) to the Hamiltonian version of the latticised O(4) non-linear sigma model. The method, which was initially developed for the accurate description of quantum many-body systems, gives rise to two distinct approximation schemes. These approaches are compared with each other as well as with some other Hamiltonian approaches. Our study of both the ground state and collective excitations leads to indications of a possible chiral phase transition as the lattice spacing is varied.Comment: 44 Pages, 14 figures. Uses Latex2e, graphicx, amstex and geometry package

Charged Higgs bosons from the 3-3-1 models and the R(D(∗))\mathcal{R}(D^{(*)}) anomalies

Several anomalies in the semileptonic B-meson decays such as $\mathcal{R}(D^{(*)})$ have been reported by $BABAR$, Belle, and LHCb collaborations recently. In this paper, we investigate the contributions of the charged Higgs bosons from the 3-3-1 models to the $\mathcal{R}(D^{(*)})$ anomalies. We find that, in a wide range of parameter space, the 3-3-1 models might give reasonable explanations to the $\mathcal{R}(D^{(*)})$ anomalies and other analogous anomalies of the B meson's semileptonic decays.Comment: Accpeted by Physical Review