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Farnell, Damian J. J.; Bishop, R. F.; Gernoth, K. A.

doi:10.1023/a:1015769622279

Cited by 55 publications

(137 citation statements)

References 58 publications

(76 reference statements)

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“…The details of the practical application of high-order coupled cluster method (CCM) formalism to lattice quantum spin systems are given in [60,64,69,74] and also in the appendices to this article. The high-order CCCM code is freely available online [73].…”

Section: Methodsmentioning

confidence: 99%

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High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J_{1}-J_{2} model

Farnell¹

2009

Condens. Matter Phys.

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In this article we present new formalism for high-order coupled cluster method (CCM) calculations for "generalized" ground-state expectation values and the excited states of quantum magnetic systems with spin quantum number s 1 2. We use high-order CCM to demonstrate spontaneous symmetry breaking in the spin-half J 1 -J 2 model for the linear chain using the coupled cluster method (CCM). We show that we are able to reproduce exactly the dimerized ground (ket) state at the Majumdar-Ghosh point (J 2 /J 1 = 1 2 ) using a Néel model state. We show that the onset of dimerized phase is indicated by a bifurcation of the nearest-neighbour ket-and bra-state correlation coefficients for the nearest-neighbour Néel model state. We show that groundstate energies are in good agreement with the results of exact diagonalizations of finite-length chains across this entire regime (i. e., J 1 > 0 and J 2 1 2). The effects of the bifurcation point are also observed for the sublattice magnetization for the nearest-neighbour model state. Finally, we use the new formalism for the excited state in order to obtain the excitation energy as a function of J 2 /J 1 for the nearest-neighbour model state by solving up to the LSUB14 level of approximation. We obtain an extrapolated value for the excited-state energy gap of −0.0036 at J 2 /J 1 = 0.0 and of 0.2310 at J 2 /J 1 = 0.5. We show that an excitation energy gap opens up at J 2 /J 1 ≈ 0.24, although the gap only becomes large at J 2 /J 1 ≈ 0.4.

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Section: Methodsmentioning

confidence: 99%

“…For example, we refer the interested reader to [64,69] for additional extensive discussions of highorder CCM for the ground and excited states. Recently, however, considerable extensions to the basic high-order formalism for quantum spin systems have also been made.…”

Section: Methodsmentioning

confidence: 99%

High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J_{1}-J_{2} model

Farnell¹

2009

Condens. Matter Phys.

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“…We refer the interested reader e.g., to Refs. 15,21, 22 and 11,[23][24][25] respectively. First we report the main theoretical results.…”

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The Magnetization Process of the Spin-One Triangular-Lattice Heisenberg Antiferromagnet

et al. 2013

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Starting with Wannier's 1) and Anderson's 2) seminal papers the triangular-lattice antiferromagnet has attracted a lot of attention. One spectacular feature of this model system for a strongly frustrated magnet is the unconventional magnetization process of the triangular-lattice Heisenberg antiferromagnet. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] While for the classical isotropic Heisenberg model at zero temperature the magnetization M increases linearly with the applied magnetic field H, thermal or quantum fluctuations induce a plateau at 1/3 of the saturation magnetization M sat (''order from disorder'' phenomenon). For the extreme quantum case, i.e., spin quantum number s ¼ 1=2, this plateau at T ¼ 0 has been widely discussed. Very recently an almost perfect experimental realization of an s ¼ 1=2 triangular-lattice Heisenberg antiferromagnet has been reported for Ba 3 CoSb 2 O 9 , 17) where the entire measured magnetization curve MðHÞ including the 1/3 plateau is in excellent agreement with theoretical predictions. In particular, the theoretical magnetization data obtained by high-order coupled-cluster approximation 11) and by large-scale exact diagonalization approach 15) almost coincide with the measured ones over a wide range of the magnetic field.Another interesting triangular-lattice magnet is Ba 3 -NiSb 2 O 9 that is considered as a good candidate of an s ¼ 1 triangular-lattice Heisenberg antiferromagnet. 16,18,19) In Ba 3 NiSb 2 O 9 , the uniform triangular lattice of magnetic ions is realized as in Ba 3 CoSb 2 O 9 . Indeed, recently it has been found that the magnetization curve of this compound also exhibits a clear 1/3 plateau. 16) By contrast to the wellinvestigated spin-half case there are much less reliable theoretical studies of the s ¼ 1 model relevant for Ba 3 NiSb 2 O 9 . Motivated by the excellent agreement of theoretical predictions based on exact diagonalization (ED) and coupled-cluster method (CCM) and experimental results for the spin-half compound Ba 3 CoSb 2 O 9 reported in Ref. 17 we apply in this paper these methods to the s ¼ 1 model to provide theoretical data to compare with experimental results.For the s ¼ 1 model the Lanczos ED for N ¼ 27 sites and the CCM-SUBn-n approximation 20) for n ¼ 2; 4; 6; 8 are used to calculate the field-dependent properties of the model.In this short note we will not explain details of the Lanczos ED and the CCM. We refer the interested reader e.g., to Refs. 15,21, 22 and 11,[23][24][25] respectively. First we report the main theoretical results. The saturation field is H sat ¼ 9Js ¼ 9J, where J is the nearest-neighbor exchange coupling. The zero-field uniform susceptibility calculated with CCM-SUBn-n approximation is ¼ 0:10790, 0.09932, 0.09785, and 0.09679 for n ¼ 2, 4, 6, and 8, respectively. Moreover, it is useful to extrapolate the ''raw'' SUBn-n data to n ! 1 by ðnÞ ¼ c 0 þ c 1 ð1=nÞ þ c 2 ð1=nÞ 2 which yields finally our CCM estimate for the susceptibility CCM ¼ 0:0956. This value is in excellent agreement with the spin-wave res...

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“…Our best results for the ground-state energy and sublattice magnetization for the pure nearest-neighbor model are given by Eg/N = −0.5534 and M = 0.19, respectively, and we predict that there is no Néel ordering in the region 0.2 ≤ J2/J1 ≤ 0.7. These results are shown to be in excellent agreement with the best results of other approximate methods.A new procedure for carrying out high-order coupled cluster method (CCM) [1,2,3,4,5,6,7,8] calculations via parallel processing is presented here. The CCM may be applied to systems demonstrating strong frustration and for arbitrary spatial dimension of the lattice.…”

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confidence: 99%

“…A new procedure for carrying out high-order coupled cluster method (CCM) [1,2,3,4,5,6,7,8] calculations via parallel processing is presented here. The CCM may be applied to systems demonstrating strong frustration and for arbitrary spatial dimension of the lattice.…”

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confidence: 99%

High-order coupled cluster calculations via parallel processing: An illustration forCaV4O9

et al. 2005

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The coupled cluster method (CCM) is a method of quantum many-body theory that may provide accurate results for the ground-state properties of lattice quantum spin systems even in the presence of strong frustration and for lattices of arbitrary spatial dimensionality. Here we present a significant extension of the method by introducing a new approach that allows an efficient parallelization of computer codes that carry out "high-order" CCM calculations. We find that we are able to extend such CCM calculations by an order of magnitude higher than ever before utilized in a high-order CCM calculation for an antiferromagnet. Furthermore, we use only a relatively modest number of processors, namely, eight. Such very high-order CCM calculations are possible only by using such a parallelized approach. An illustration of the new approach is presented for the ground-state properties of a highly frustrated two-dimensional magnetic material, CaV4O9. Our best results for the ground-state energy and sublattice magnetization for the pure nearest-neighbor model are given by Eg/N = −0.5534 and M = 0.19, respectively, and we predict that there is no Néel ordering in the region 0.2 ≤ J2/J1 ≤ 0.7. These results are shown to be in excellent agreement with the best results of other approximate methods.A new procedure for carrying out high-order coupled cluster method (CCM) [1,2,3,4,5,6,7,8] calculations via parallel processing is presented here. The CCM may be applied to systems demonstrating strong frustration and for arbitrary spatial dimension of the lattice. We illustrate our new approach by applying it to CaV 4 O 9 [9,10,11,12,13,14,15] at zero temperature. An increasing number of insulating quantum magnetic systems for lattices of low spatial dimensionality are being studied experimentally. Indeed, the calcium vanadium oxide (CAVO) materials are one particularly useful example. They exhibit strong frustration for a number of different crystallographic lattices with respect to varying chemical composition, and they may demonstrate "novel" groundstate ordering. Indeed, theoretical evidence suggests that CAVO systems may contain a number of differing quantum ground states (see, e.g., Refs. [9,11]) at zero temperature as a function of varying nearest-neighbor nextnearest-neighbor bond strengths. The relevant Hamiltonian is given bywhere i runs over all lattice sites, and j and k run over all nearest-neighbor and next-nearest-neighbor sites to i, respectively, counting each bond once and once only. The bond strengths are given by J 1 and J 2 for nearestneighbor and next-nearest-neighbor terms, respectively. The lattice and exchange "bonds" are illustrated graphically in Fig. 1. For this model, collinear Néel ordering is observed with respect to nearest neighbors at J 1 > 0 and J 2 = 0 and with respect to next-nearest neighbors at J 2 > 0 and diate phase (or phases) for 0.2 < J 2 /J 1 < 0.7, which is also in good agreement with results of a "spin-wave theory-like" treatment [9] that predict such an intermediate regime for 0.25 < J 2 ...

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Cited by 55 publications

References 58 publications

High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J_{1}-J_{2} model

High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J_{1}-J_{2} model

The Magnetization Process of the Spin-One Triangular-Lattice Heisenberg Antiferromagnet

High-order coupled cluster calculations via parallel processing: An illustration forCaV4O9

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