arXiv subjects

D. J. J. Farnell

Publications and source records attributed to D. J. J. Farnell.

At least 19 recordsLinked to original sources

arXiv2018

Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method

Coplanar model states for applications of the coupled cluster method (CCM) to problems in quantum magnetism are those in which all spins lie in a plane, whereas three-dimensional (3D) model states are, by contrast, non-coplanar ones in which all the spins do not lie in any single plane. Here we extend the CCM to non-coplanar / 3D model states and we present results for three cases: (a) the spin-half one-dimensional Ising ferromagnet in an applied transverse magnetic field (as an exactly solvable test model to use as a yardstick for the viability and accuracy of our new methodology); (b) the spin-half triangular-lattice Heisenberg antiferromagnet in the presence of an external magnetic field; and (c) the spin-$S$ triangular-lattice {\it XXZ} antiferromagnet in the presence of an external magnetic field, for the cases $\frac{1}{2} \leq S \leq5 $. For 3D model states the sets of algebraic CCM equations for the ket- and bra-state correlation coefficients become complex-valued, but ground-state expectation values of all physical observables are manifestly real numbers, as required. Excellent correspondence is seen with the results of other methods, where they exist, for these systems. CCM results demonstrate explicitly that coplanar ordering is favoured over non-coplanar ordering for the triangular-lattice spin-half Heisenberg antiferromagnet at all values of the applied external magnetic field, whereas for the anisotropic {\it XXZ} model non-coplanar ordering can be favoured in some regions of the parameter space. Specifically, we present a precise determination of the boundary (i.e., the critical value of the {\it XXZ} anisotropy parameter $Δ$) between a 3D ground state and a coplanar ground state for the {\it XXZ} model for values for the external magnetic field near to saturation, for values of the spin quantum number $S \leq 5$.

cond-mat.str-el↗

arXiv2018

The Interplay Between Lattice Topology, Frustration, and Spin Quantum Number in Quantum Antiferromagnets on Archimedean Lattices

The interplay between lattice topology, frustration, and spin quantum number, $s$, is explored for the Heisenberg antiferromagnet (HAFM) on the eleven two-dimensional Archimedean lattices (square, honeycomb, CaVO, SHD, SrCuBO, triangle, bounce, trellis, maple-leaf, star, and kagome). We show the CCM provides consistently accurate results when compared to the results of other approximate methods. The $\sqrt{3}\times\sqrt{3}$ model state provides lower ground-state energies than those of the $q=0$ model state for the kagome and star lattices for most values of $s$. The $q=0$ model state provides lower ground-state energies only for $s=1/2$ for the kagome lattice and $s=1/2$ and $s=1$ for the star lattice. The kagome and star lattices demonstrate the least amount of magnetic ordering and the unfrustrated lattices (square, honeycomb, SHD, and CaVO) demonstrate the most magnetic ordering for all values of $s$. The SrCuBO and triangular lattices also demonstrate high levels of magnetic ordering, while the remaining lattices (bounce, maple-leaf, and trellis) tend to lie between these extremes, again for all values of $s$. These results also clearly reflect the strong increase in magnetic order with increasing spin quantum number $s$ for all lattices. The ground-state energy, $E_g/(NJs^2)$, scales with $s^{-1}$ to first order, as expected from spin-wave theory, although the order parameter, $M/s$, scales with $s^{-1}$ for most of the lattices only. Self-consistent spin-wave theory calculations indicated previously that $M/s$ scales with $s^{-2/3}$ for the kagome lattice HAFM, whereas previous CCM results (replicated here also) suggested that $M/s$ scales with $s^{-1/2}$. By using similar arguments, we find here also that $M/s$ scales with $s^{-1/3}$ on the star lattice and with $s^{-2/3}$ on the SrCuBO lattice.

cond-mat.str-el↗

arXiv2016

Ground-State Ordering of the $J_1$--$J_2$ Model on the Simple Cubic and Body-Centered Cubic Lattices

The $J_1$--$J_2$ Heisenberg model is a "canonical" model in the field of quantum magnetism in order to study the interplay between frustration and quantum fluctuations as well as quantum phase transitions driven by frustration. Here we apply the Coupled Cluster Method (CCM) to study the spin-half $J_1$--$J_2$ model with antiferromagnetic nearest-neighbor bonds $J_1 >0$ and next-nearest-neighbor bonds $J_2 >0$ for the simple cubic (SC) and body-centered cubic (BCC) lattices. In particular, we wish to study the ground-state ordering of these systems as a function of the frustration parameter $p=z_2J_2/z_1J_1$, where $z_1$ ($z_2$) is the number of nearest (next-nearest) neighbors. We wish to determine the positions of the phase transitions using the CCM and we aim to resolve the nature of the phase transition points. We consider the ground-state energy, order parameters, spin-spin correlation functions as well as the spin stiffness in order to determine the ground-state phase diagrams of these models. We find a direct first-order phase transition at a value of $p = 0.528$ from a state of nearest-neighbor Néel order to next-nearest-neighbor Néel order for the BCC lattice. For the SC lattice the situation is more subtle. CCM results for the energy, the order parameter, the spin-spin correlation functions and the spin stiffness indicate that there is no direct first-order transition between ground-state phases with magnetic long-range order, rather it is more likely that two phases with antiferromagnetic long-range are separated by a narrow region of a spin-liquid like quantum phase around $p=0.55$. Thus the strong frustration present in the $J_1$--$J_2$ Heisenberg model on the SC lattice may open a window for an unconventional quantum ground state in this three-dimensional spin model.

cond-mat.str-el↗

arXiv2015

Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number $s$

We apply the coupled cluster method to high orders of approximation and exact diagonalizations to study the ground-state properties of the triangular-lattice spin-$s$ Heisenberg antiferromagnet. We calculate the fundamental ground-state quantities, namely, the energy $e_0$, the sublattice magnetization $M_{\rm sub}$, the in-plane spin stiffness $ρ_s$ and the in-plane magnetic susceptibility $χ$ for spin quantum numbers $s=1/2, 1, \ldots, s_{\rm max}$, where $s_{\rm max}=9/2$ for $e_0$ and $M_{\rm sub}$, $s_{\rm max}=4$ for $ρ_s$ and $s_{\rm max}=3$ for $χ$. We use the data for $s \ge 3/2$ to estimate the leading quantum corrections to the classical values of $e_0$, $M_{\rm sub}$, $ρ_s$, and $χ$. In addition, we study the magnetization process, the width of the 1/3 plateau as well as the sublattice magnetizations in the plateau state as a function of the spin quantum number $s$.

cond-mat.str-el↗

arXiv2014

The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue

We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J_1-J_2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J_2^{c1}=0.454J_1 and J_2^{c2}= 0.588 J_1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J_2 \le 0.49J_1 and J_2 > 0.58J_1. This finding is in favor of a gapless spin-liquid ground state in this parameter regime.

cond-mat.str-el↗

arXiv2013

Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States

We investigate ground states of $s$=1/2 Heisenberg antiferromagnets on the eleven two-dimensional (2D) Archimedian lattices by using the coupled cluster method. Magnetic interactions and quantum fluctuations play against each other subtly in 2D quantum magnets and the magnetic ordering is thus sensitive to the features of lattice topology. Archimedean lattices are those lattices that have 2D arrangements of regular polygons and they often build the underlying magnetic lattices of insulating quasi-two-dimensional quantum magnetic materials. Hence they allow a systematic study of the relationship between lattice topology and magnetic ordering. We find that the Archimedian lattices fall into three groups: those with semiclassical magnetic ground-state long-range order, those with a magnetically disordered (cooperative quantum paramagnetic) ground state, and those with a fragile magnetic order. The most relevant parameters affecting the magnetic ordering are the coordination number and the degree of frustration present.

cond-mat.str-el↗

arXiv2012

Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice

We use the coupled cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2 moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants $J_{1}>0$ along two of the three lattice directions and $J_{2} \equiv κJ_{1} > 0$ along the third. In the classical limit the ground-state (GS) phase for $κ< 1/2$ has collinear ferrimagnetic (Néel$'$) order where the $J_2$-coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $κ> 1/2$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin-1/2 case we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $κ$, namely for $0<κ<κ_{c_1}$ for the Néel$'$ state and for (at least part of) the region $κ>κ_{c_2}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region $κ_{c_1} < κ< κ_{c_2}$, which includes the isotropic kagome point $κ= 1$ where the stable GS phase is now believed to be a topological ($\mathbb{Z}_2$) spin liquid. Our best numerical estimates are $κ_{c_1} = 0.515 \pm 0.015$ and $κ_{c_2} = 1.82 \pm 0.03$.

cond-mat.str-el↗

arXiv2012

The magnetization process of the spin-one triangular-lattice Heisenberg antiferromagnet

We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.

cond-mat.str-el↗

arXiv2012

Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: the $J_{1}$--$J_{2}$--$J_{3}$ model

We use the coupled cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 $J_{1}$--$J_{2}$--$J_{3}$ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local on-site magnetization. With the nearest-neighbor coupling strength $J_{1} \equiv 1$ we find four magnetically ordered phases in the parameter window $J_{2},J_{3} \in [0,1]$, namely the Néel (N), striped (S), and anti-Néel (aN) collinear AFM phases, plus a spiral phase. The aN phase appears as a stable GS phase in the classical version of the model only for values $J_{3}<0$. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at: (a) $(J_{2}^{c_1},J_{3}^{c_1})=(0.51 \pm 0.01,0.69 \pm 0.01)$ between the N, S, and QP phases; (b) $(J_{2}^{c_2},J_{3}^{c_2})=(0.65 \pm 0.02,0.55 \pm 0.01)$ between the S, spiral, and QP phases; and (c) $(J_{2}^{c_3},J_{3}^{c_3})=(0.69 \pm 0.01,0.12 \pm 0.01)$ between the spiral, aN, and QP phases.

cond-mat.str-el↗

arXiv2012

The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_{1}$--$J_{2}$ model

We study the ground-state (gs) phases of the spin-half anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is a frustrated antiferromagnetic (AFM) $J_{1}$--$J_{2}$ system on the checkerboard lattice, with nearest-neighbor exchange bonds $J_{1}>0$ and next-nearest-neighbor bonds $J_{2} \equiv κJ_{1} > 0$. Using various AFM classical ground states as CCM model states we present results for their gs energy, average on-site magnetization, and susceptibilities to plaquette valence-bond crystal (PVBC) and crossed-dimer valence-bond crystal (CDVBC) ordering. We show that the state with Neel ordering is the gs phase for $κ< κ_{c_1} \approx 0.80 \pm 0.01$, but that none of the fourfold set of AFM states selected by quantum fluctuations at $O(1/s)$ in a large-$s$ analysis (where $s$ is the spin quantum number) from the infinitely degenerate set of AFM states that form the gs phase for the classical version of the model (for $κ>1$) survives the quantum fluctuations to form a stable magnetically-ordered gs phase for the spin-half case. The Neel state becomes susceptible to PVBC ordering at or very near to $κ= κ_{c_1}$, and the fourfold AFM states become infinitely susceptible to PVBC ordering at $κ= κ_{c_2} \approx 1.22 \pm 0.02$. In turn, we find that these states become infinitely susceptible to CDVBC ordering for all values of $κ$ above a certain critical value at or very near to $κ= κ_{c_2}$. We thus find a Neel-ordered gs phase for $κ<κ_{c_1}$, a PVBC-ordered phase for $κ_{c_1} < κ< κ_{c_2}$, and a CDVBC-ordered phase for $κ> κ_{c_2}$. Both transitions are probably direct ones, although we cannot exclude very narrow coexistence regions confined to $0.79 \lesssim κ\lesssim 0.81$ and $1.20 \lesssim κ\lesssim 1.22$ respectively.

cond-mat.str-el↗

arXiv2012

Ground-state phases of the frustrated spin-1/2 $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg ferromagnet ($J_{1}<0$) on the honeycomb lattice with $J_{3}=J_{2}>0$

We study the ground-state (gs) properties of the frustrated spin-1/2 $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg model on a honeycomb lattice with ferromagnetic (FM) nearest-neighbor ($J_{1}=-1$) exchange and frustrating antiferromagnetic (AFM) next-nearest-neighbor ($J_{2}>0$) and next-next-nearest-neighbor ($J_{3}>0$) exchanges, for the case $J_{3}=J_{2}$. We use the coupled cluster method in high orders of approximation, complemented by the exact diagonalization of a lattice with 32 sites, and calculate the gs energy, magnetic order parameter, and spin-spin correlation functions. We find a quantum phase transition between regions characterized by FM order and a form of AFM ("striped") collinear order at $J^{c}_{2} \approx 0.1095 \pm 0.0005$. We compare results for the FM case (with $J_{1}=-1$) to previous results for the corresponding AFM case (with $J_{1}=+1$). While the magnetic order parameters behave similarly for the FM and the AFM models for large values of the frustration parameter $J_{2}$, there are considerable differences between them for $J_{2}/|J_{1}| \lesssim 0.6$. For example, the quasiclassical collinear magnetic long-range order for the AFM model (with $J_{1}=+1$) breaks down at $J^{c_{2}}_{2} \approx 0.60$, whereas the "equivalent" point for the FM model (with $J_{1}=-1$) occurs at $J^{c}_{2} \approx 0.11$. Unlike in the AFM model (with $J_{1}=+1$), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical AFM phases (with Néel and striped order) for $J^{c_{1}}_{2} < J_{2} < J^{c_{2}}_{2}$, with $J^{c_{1}}_{2} \approx 0.47$, we find no clear indications in the FM model for an intermediate magnetically disordered phase between the phases exhibiting FM and striped order. Instead, the evidence points strongly to a direct first-order transition between the two ordered phases of the FM model.

cond-mat.str-el↗

arXiv2012

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_{1}$--$J_{2}$ model

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=κJ_1>0$ ($J_{1}>0$) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for $κ_{c_1}<κ<κ_{c_2}$, where $κ_{c_1} \approx 0.207 \pm 0.003$ and $κ_{c_2} \approx 0.385 \pm 0.010$. The transition at $κ_{c_1}$ to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range $0.21 \lesssim κ\lesssim 0.24$), while that at $κ_{c_2}$ is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point $κ= 1/2$. The spiral phases that are present classically for all values $κ> 1/6$ are absent for all $κ\lesssim 1$.

cond-mat.str-el↗

arXiv2011

The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment

Starting with the sqrt{3} x sqrt{3} and the q=0 states as reference states we use the coupled cluster method to high orders of approximation to investigate the ground state of the Heisenberg antiferromagnet on the kagome lattice for spin quantum numbers s=1/2,1,3/2,2,5/2, and 3. Our data for the ground-state energy for s=1/2 are in good agreement with recent large-scale density-matrix renormalization group and exact diagonalization data. We find that the ground-state selection depends on the spin quantum number s. While for the extreme quantum case, s=1/2, the q=0 state is energetically favored by quantum fluctuations, for any s>1/2 the sqrt{3} x sqrt{3} state is selected. For both the sqrt{3} x sqrt{3} and the q=0 states the magnetic order is strongly suppressed by quantum fluctuations. Within our coupled cluster method we get vanishing values for the order parameter (sublattice magnetization) M for s=1/2 and s=1, but (small) nonzero values for M for s>1. Using the data for the ground-state energy and the order parameter for s=3/2,2,5/2, and 3 we also estimate the leading quantum corrections to the classical values.

cond-mat.str-el↗

arXiv2011

The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J $ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.

cond-mat.str-el↗

arXiv2011

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =κJ_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a Néel antiferromagnetic (AFM) phase for $κ< κ_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $κ> κ_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $κ_{c_{1}} \lesssim κ\lesssim κ_{c_{2}}$. The transition at $κ_{c_{2}}$ appears to be of first-order type, while that at $κ_{c_{1}}$ is continuous. Since the Néel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at $κ_{c_{1}}$.

cond-mat.str-el↗

arXiv2010

Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet

The coupled cluster method is applied to a spin-half model at zero temperature ($T=0$), which interpolates between Heisenberg antiferromagnets (HAF's) on a kagome and a square lattice. With respect to an underlying triangular lattice the strengths of the Heisenberg bonds joining the nearest-neighbor (NN) kagome sites are $J_{1} \geq 0$ along two of the equivalent directions and $J_{2} \geq 0$ along the third. Sites connected by $J_{2}$ bonds are themselves connected to the missing NN non-kagome sites of the triangular lattice by bonds of strength $J_{1}' \geq 0$. When $J_{1}'=J_{1}$ and $J_{2}=0$ the model reduces to the square-lattice HAF. The magnetic ordering of the system is investigated and its $T=0$ phase diagram discussed. Results for the kagome HAF limit are among the best available.

cond-mat.str-el↗

arXiv2010

Magnetic order on a frustrated spin-1/2 Heisenberg antiferromagnet on the Union Jack lattice

We use the coupled cluster method (CCM) to study the zero-temperature phase diagram of a 2D frustrated spin-half antiferromagnet, the so-called Union Jack model. It is defined on a square lattice such that all nearest-neighbor bonds are present with a strength $J_{1} > 0$, but only half the next-nearest-neighbor bonds are present with a strength $J_{2} \equiv κJ_{1} > 0$. The bonds are arranged such that on the $2 \times 2$ unit cell they form the pattern of the Union Jack flag. We find strong evidence for a first phase transition between a Néel phase and a canted ferrimagnetic phase at a critical coupling $κ_{c_{1}} = 0.66 \pm 0.02$. At the transition the energy and its first derivative seem continuous, thus providing a typical scenario of a second-order transition, although a weakly first-order transition cannot be excluded. By contrast, the average on-site magnetization $M$ approaches a nonzero value $M_{c_{1}}=0.195 \pm 0.005$ on both sides of the transition, which is more typical of a first-order transition. The slope $dM/dκ$ also appears to be continuous, or very nearly so, at the critical point $κ_{c_{1}}$. We find strong evidence that the canted phase becomes unstable at large values of $κ$, and hence we have also used the CCM with a model collinear semi-stripe-ordered ferrimagnetic state in which alternating rows (and columns) are ferromagnetically and antiferromagnetically ordered. We find tentative evidence, based on the relative energies of the two states, for a second (first-order) phase transition between the canted and semi-stripe-ordered states at a large value of the coupling parameter around $κ_{c_{2}} \approx 125 \pm 5$. This prediction, however, is based on an extrapolation of the CCM results for the canted state into regimes where the CCM equations at any level of approximation beyond the lowest have no solutions.

cond-mat.str-el↗

arXiv2010

High-Order Coupled Cluster Method (CCM) Formalism 3: Finite-Size CCM

Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body spin operators. An advantage of the CCM is that the Goldstone linked-cluster theorem is obeyed at all levels of approximation and so it provides results in the infinite lattice limit $N \to \infty$ from the outset. However, recent results have also shown that the CCM can provide exact (symmetry-breaking) results for the spin-half linear-chain $J_1$--$J_2$ at the Majumdar-Ghosh point $J_2/J_1=0.5$ by identifying special solutions of the CCM equations for the usual Néel model state. Interestingly, the CCM provides exact (non-symmetry-breaking) results for systems in which small magnetic clusters become de-coupled from each other when the bonds connecting them tend to zero. These exact results involve the identification of "special solutions" of the CCM equations for the Néel state. An example of this is given by a spin-half system with nearest-neighbour bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO) in which one of the two different types of bonds on the lattice tend to zero. Larger finite-sized systems may be considered by appropriate choice of the unit cell and the bonds on it. We show here that exact diagonalisation results for ground-state energy and excitation energy gap for the spin-half and spin-one linear Heisenberg model on chains of length up to N=12 sites for s=1/2 and N=6 sites for s=1 with periodic boundary conditions are reproduced exactly using high-order CCM via this "brute-force" approach; i.e., one in which none of the translational or point-group symmetries of the finite lattice are used.

cond-mat.str-el↗