Spin-Wave Spectrum of the Antiferromagnetic Linear Chain

Cloizeaux, J. des; Pearson, Jonathan

doi:10.1103/physrev.128.2131

Cited by 875 publications

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“…Fig.3 shows the spin-triplet excitation spectrum for spin- 1 2 with the chain size 512 and the cluster size n up to 4. The EPT calculation almost converged at n = 4, and gives an agreement of 1% precision with BA [12]. The ground state used is from p=20.…”

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confidence: 67%

“…From top to bottom, the cluster size is 1 to 4 (red online). The thick line (blue online) is the Bethe ansatz result [12]. Fig.4 shows the same for spin-1 up to the cluster size n = 3 where the calculation almost converged.…”

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confidence: 74%

“…In particular, Haldane conjectured in 1983 that the half-odd integer and integer spins might behave essentially differently [3], which together with a field theoretic prediction of Affleck [4] for a logarithmic correction to the power-law behavior in the spin-spin correlation function in the spin-1 2 case, triggered an intensive study of HA ranging from the exact diagonalization [5,6] and Monte Carlo [7,8] to DMRG (density matrix renormalization group) [9][10][11]. These studies along with the Bethe ansatz solution for the spin-1 2 case [12] lead to a confirmation of the both claims. Concerning the elementary excitation for the entire Brillouin zone, however, Takahashi's two attempts following the Feynman variational method for 4 He and a projector-Monte Carlo method were the only studies [13,14].…”

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confidence: 99%

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Entanglement perturbation theory for the elementary excitation in one dimension

Chung¹,

Wang²

2009

Physics Letters A

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The entanglement perturbation theory is developed to calculate the excitation spectrum in one dimension. Applied to the spin-1 2 antiferromagnetic Heisenberg model, it reproduces the des CloiseauxPearson Bethe ansatz result. As for spin-1, the spin-triplet magnon spectrum has been determined for the first time for the entire Brillouin zone, including the Haldane gap at k = π.PACS numbers: 71.10. Li, 02.90.+p, 71.10.Fd, 75.10.Jm The importance of elementary excitations in condensed matter systems may be best understood in the superfluid 4 He. The Tisza two-fluid model with the experimentally found phonon-roton spectrum explains fundamental properties of the superfluid 4 He [1]. Feynman's effort then to explain the roton spectrum is well known [2]. From the theorem of Bloch-Floquet, the elementary excitation with momentum k for a translationally invariant Hamiltonian H is written aswhere |g is the ground state and the summation over l extends over the entire lattice sites. The O l is a local cluster operator to be determined for a given Hamiltonian.In spite of a simplicity and validity of the expression (1), not much progress has been made along this line since the days of Feynman. The Heisenberg antiferromagnet (HA) described by the Hamiltonianis probably the best studied system concerning the excitation spectrum. In particular, Haldane conjectured in 1983 that the half-odd integer and integer spins might behave essentially differently [3], which together with a field theoretic prediction of Affleck [4] for a logarithmic correction to the power-law behavior in the spin-spin correlation function in the spin-1 2 case, triggered an intensive study of HA ranging from the exact diagonalization [5,6] and Monte Carlo [7,8] to DMRG (density matrix renormalization group) [9][10][11]. These studies along with the Bethe ansatz solution for the spin-1 2 case [12] lead to a confirmation of the both claims. Concerning the elementary excitation for the entire Brillouin zone, however, Takahashi's two attempts following the Feynman variational method for 4 He and a projector-Monte Carlo method were the only studies [13,14]. And none of the previous studies gave a serious consideration to the expression (1).In this Letter, we analyze (1) exactly for the HA (2) with periodic boundary conditions by the recently developed entanglement perturbation theory (EPT). EPT is a novel many-body method which takes into account correlations systematically. Its mathematical implementation is singular value decomposition (SVD), intuitively divide and conquer. EPT has addressed so far classical statistical mechanics [15], 1D quantum ground states [16] and 2D quantum ground states [17]. We here address the elementary excitation in one dimension. By EPT, we are not only free from a negative sign problem which is inherent to MC for quantum spins and fermions, but can also handle an order of magnitude larger systems than MC and DMRG. The key of the success lies in our ability of calculating the ground state |g precisely and most importantly in an u...

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confidence: 74%

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Entanglement perturbation theory for the elementary excitation in one dimension

Chung¹,

Wang²

2009

Physics Letters A

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“…The equations for the bra-state configuration coefficients retained in any particular approximation are now obtained exactly as before by taking the overlap of the Schrodinger equation, <~IH = E <~I , (25) g with each of the ket-state wavefunctions corresponding to the particular configurations retained.…”

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confidence: 99%

“…Specifically, we mostly antiferromagnets described by the both lD chains and the 20 square as the special (isotropic) 25 We have briefly reviewed some of these exact results elsewhere. 2&…”

Section: Introductionmentioning

confidence: 99%

Correlations in Quantum Spin Chains and Lattices: A Fully Microscopic Many-Body Approach

Bishop

Parkinson

Xian

1992

Recent Progress in Many-Body Theories

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Numerical solution for the ground-state energy of the anisotropic Heisenberg model

Bracken

1997

Int. J. Quantum Chem.

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An analysis of the anisotropic Heisenberg model is carried out by solving the Bethe ansatz solution of the model numerically as a function of the anisotropy parameter for finite N. A brief introduction to the limit of the infinite chain is presented. The energy for a few special limiting cases of the anisotropy parameter in the Hamiltonian are worked out. Numerical results for finite cycles as well as for the infinite chain are given. Comparison can then be made with the case of finite increasing N.

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Spin-Wave Spectrum of the Antiferromagnetic Linear Chain

Cited by 875 publications

References 4 publications

Entanglement perturbation theory for the elementary excitation in one dimension

Entanglement perturbation theory for the elementary excitation in one dimension

Correlations in Quantum Spin Chains and Lattices: A Fully Microscopic Many-Body Approach

Numerical solution for the ground-state energy of the anisotropic Heisenberg model

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