Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State

Haldane, F. D. M.

doi:10.1103/physrevlett.50.1153

Cited by 3,542 publications

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“…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.…”

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confidence: 99%

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: 99%

Entanglement perturbation theory for the elementary excitation in one dimension

Chung¹,

Wang²

2009

Physics Letters A

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“…In this case, the Haldane state and the LD state of H (2) eff correspond to the ID state and the LD state of the present S = 2 model, respectively. The multicritical point among the Haldane, LD and Néel phases of H (2) eff is (∆ eff , D 2,eff ) (3.2, 2.9) [22], which reads (∆, D 4 ) (9.4, 8.7).…”

Section: Discussionmentioning

confidence: 84%

“…The multicritical point among the Haldane, LD and Néel phases of H (2) eff is (∆ eff , D 2,eff ) (3.2, 2.9) [22], which reads (∆, D 4 ) (9.4, 8.7). Thus the multicritical point among the ID, LD and Néel phases in Fig.3(c) is well explained.…”

Section: Discussionmentioning

confidence: 99%

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Edge Modes in the Intermediate-D and Large-D Phases of the S = 2 Quantum Spin Chain with XXZ and On-Site Anisotropies

Okamoto

Tonegawa

Sakai

et al. 2014

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

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We investigate the edge modes at T = 0 in the intermediate-D (ID) phase and the large-D (LD) phase of the S = 2 quantum spin chain with the XXZ anisotropy and the generalized on-site anisotropies by use of the DMRG. There exists a gapless edge mode in the ID phase, while no gapless edge mode in the LD phase. These results are consistent with the physical pictures of these phases. We also show the ground-state phase diagrams obtained by use of the exact diagonalization and the level spectroscopy analysis.

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“…It thus came as a surprise when Haldane conjectured in 1983 that quantum Heisenberg antiferromagnetic chains have qualitatively different properties according to whether the spin value is integer or half-integer [3].…”

Section: Introductionmentioning

confidence: 99%

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

2016

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In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives. An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured. In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.

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Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State

Cited by 3,542 publications

References 12 publications

Entanglement perturbation theory for the elementary excitation in one dimension

Entanglement perturbation theory for the elementary excitation in one dimension

Edge Modes in the Intermediate-D and Large-D Phases of the S = 2 Quantum Spin Chain with XXZ and On-Site Anisotropies

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

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