Ground-State of Spin-1/2 Alternating Heisenberg-<i>XY</i>Ferromagnet in One Dimension

Okamoto, Ken‐ichi; Sugiyama, Tadao

doi:10.1143/jpsj.57.1610

Cited by 12 publications

(3 citation statements)

References 28 publications

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“…At ∆ = −1/ √ 2, δ = 0, the critical dimension of sin √ 2φ becomes marginal. Therefore, in the neighborhood of this point, there appears the BKT transition [40]. Although there exist higher terms such as cos √ 8φ, we neglect them for simplicity.…”

Section: Bond-alternation S=1/2 Spin Chainmentioning

confidence: 99%

Correlation functions of the 2D sine-Gordon model

Nomura¹

1995

J. Phys. A: Math. Gen.

103

132

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A number of two-dimensional(2D) critical phenomena can be described in terms of the 2D sine-Gordon model. With the bosonization, several 1D quantum systems are also transformed to the same model. However, the transition of the 2D sine-Gordon model, Berezinskii-KosterlitzThouless(BKT) transition, is essentially different from the second-order transition. The divergence of the correlation length is more rapid than any power-law, and there are logarithmic corrections. These pathological features make difficult to determine the BKT transition point and critical indices from finite-size calculations. In this paper, we calculate the several correlation functions of this model using a real-space renormalization technique. It is found that the several correlation functions, or eigenvalues of the corresponding transfer matrix for a finite system, become degenerate on the BKT line including logarithmic corrections. By the use of this degeneracy, which reflects the hidden SU(2) symmetry on the BKT line,it is possible to determine the BKT critical line with high precision from small size data, and to identify the universality class. In addition, a new universal relation is found. This reveals the relation between the Abelian and the non-Abelian bosonization.

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Section: Bond-alternation S=1/2 Spin Chainmentioning

confidence: 99%

Correlation functions of the 2D sine-Gordon model

Nomura¹

1995

J. Phys. A: Math. Gen.

103

132

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“…4. This phase diagram was obtained by the renormalization group calculation, 6 by the high temperature series expansion after mapping H (d) onto the finite-temperature classical 2D model (modified Ashkin-Teller model), 7 and by the numerical diagonalization of the original spin Hamiltonian for finite systems. 8 When δ…”

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confidence: 99%

Plateau of the magnetization curve of the ferromagnetic-ferromagnetic-antiferromagnetic spin chain

Okamoto

1996

Solid State Communications

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I analytically study the plateau of the magnetization curve at M/M S = 1/3 (where M S is the saturation magnetization) of the one-dimensional S = 1/2 trimerized Heisenberg spin system with ferromagnetic (J F )-ferromagnetic (J F )-antiferromagnetic (J A ) interactions at T = 0. I use the bosonization technique for the fermion representation of the spin Hamiltonian through the Jordan-Wigner transformation. The plateau appears when γ ≡ J F /J A < γ C , and vanishes when γ > γ C , where the critical value γ C is estimated as γ C = 5 ∼ 6. The behavior of the width of the plateau near γ C is of the Kosterlitz-Thouless type. The present theory well explains the numerical result by Hida.

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“…This type of singlet dimer survives to λ = −1/ √ 2 = −0.707 in the S = 1/2 bond-alternating XXZ chain 14,15 . Further, if we neglect J 3 , the present system becomes a trimerized S = 1/2 XXZ chain, in which Okamoto and Kitazawa 16 showed that the no-plateau state appears for λ < −0.729.…”

Section: Discussionmentioning

confidence: 94%

Magnetization Plateau of the Distorted Diamond Spin Chain

Ueno

Zenda

Tachibana

et al. 2020

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)

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The frustrated quantum spin system on the distorted diamond chain lattice is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. In the previous work this system was revealed to exhibit the 1/3 magnetization plateau due to two different mechanisms depending on the coupling parameters, and the phase diagram at the 1/3 magnetization was obtained. In the present work it is found that the 1/3 magnetization plateau vanishes for sufficiently large XY -like coupling anisotropy. The phase diagram based on the level spectroscopy analysis is also presented.

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Ground-State of Spin-1/2 Alternating Heisenberg-XYFerromagnet in One Dimension

Cited by 12 publications

References 28 publications

Correlation functions of the 2D sine-Gordon model

Correlation functions of the 2D sine-Gordon model

Plateau of the magnetization curve of the ferromagnetic-ferromagnetic-antiferromagnetic spin chain

Magnetization Plateau of the Distorted Diamond Spin Chain

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