A microscopic approach to the dimerization in frustrated spin- 1/2 antiferromagnetic chains

Xian, Yang

doi:10.1088/0953-8984/6/30/015

Cited by 33 publications

(65 citation statements)

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“…The ground-state properties of this system have been studied using methods such as exact diagonalizations [2,7], DMRG [3][4][5]55], CCM [8,52,54,78,85], and field-theoretical approaches [5] (see [5,6] for a general review). Note that previous CCM studies of the model considering only independent-spin product model states that conserve the lattice symmetry are reported in [52,79].…”

Section: Introductionmentioning

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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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: Introductionmentioning

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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“…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.…”

mentioning

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%

“…(4) and (5) for the ket and bra states, respectively, where (8) and where N f is the number of fundamental configurations. There are therefore N f equations for both f I andf I , which refer to the ket and bra states, respectively.…”

mentioning

confidence: 99%

“…Our approach is to iterate directly the set of equations in (7) to convergence first in order to obtain the ket-state correlation coefficients. We then iterate directly the set of equations in (8) to convergence in order to obtain values for the bra-state correlation coefficients. Our parallelization technique is now to split the problem of determining and solving the N f equations for both the bra and ket states of Eqs.…”

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confidence: 99%

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

et al. 2009

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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. Néel) 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, and results for the ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains in this regime. We present evidence of symmetry breaking by considering the ket-and bra-state correlation coefficients as a function of J 2 /J 1 . A radical change is also observed in the behavior of the CCM sublattice magnetization as we enter the dimerized phase. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases.Once again, very good results for the ground-state energies are obtained. We find CCM critical points of the bra-state equations that are in agreement with the known phase transition point for this model. The results for the sublattice magnetization remain near to the "true" value of zero over much of the dimerized regime, although they diverge exactly at the critical point. 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, Néel-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. Furthermore, we estimate the range over which the Néel order is stable, and we find the CCM result is in reasonable agreement with the results obtained by other methods.Our new approach has the dual advantages that it is simple to implement and that existing CCM codes for independent-spin product model states may be used from the outset. Furthermore, it also greatly extends the range of applicability to which the CCM may be applied. We believe that the CCM now provides an excellent choice of method for the study of systems with valence-bond quantum ground states.

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A microscopic approach to the dimerization in frustrated spin- 1/2 antiferromagnetic chains

Cited by 33 publications

References 36 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

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

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

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