Correlation functions of the 2D sine-Gordon model

Nomura, K.

doi:10.1088/0305-4470/28/19/003

Cited by 103 publications

(140 citation statements)

References 54 publications

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“…We carefully estimated the errors of both critical lines by trying the extrapolation to N → ∞ choosing various sets of system sizes among N = 16, 14, 12, 10 and 8 as shown in gapless transition, the critical points are difficult to determine. Following the procedure proposed by Nomura [3,6,7,8], the critical point is determined by the crossing point of the excitation energy of the lowest excitation ∆E 3 with M z = 4, P = 1, k = 0 and ∆E 0 with M z = 0, P = 1, k = 0 where k is the wave number of the excitation.…”

Section: The Hamiltonian Is Given Bymentioning

confidence: 99%

“…In spite of its long history of the study and fundamental importance, however, a quantitatively reliable phase diagram of this model has not yet been published. In the present work, we present the quantitative phase diagram of this model analyzing the exact diagonalization data by various methods including the recently developed level spectroscopy method [3] based on conformal field theory and renormalization group. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Ground-state phase diagram ofS=1XXZchains with uniaxial single-ion-type anisotropy

2003

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One dimensional S = 1 XXZ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization group and finite size scaling method. We thus present the first quantitatively reliable ground state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, Néel phase, two XY phases and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless type transitions, the Gaussian type transitions, the Ising type transitions and the first order transitions. The location of these critical lines are accurately determined.

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Section: The Hamiltonian Is Given Bymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ground-state phase diagram ofS=1XXZchains with uniaxial single-ion-type anisotropy

2003

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“…But the level spectroscopy method [5] [6] has been proposed to resolve these problems. Near a BKT transition point, some scaling dimensions change from relevant to irrelevant or vice versa.…”

Section: Introductionmentioning

confidence: 99%

Berezinskii–Kosterlitz–Thouless transitions in the six-state clock model

Matsuo¹,

Nomura²

2006

J. Phys. A: Math. Gen.

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Classical 2D clock model is known to have a critical phase with Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty, one of the authors has proposed the method called level spectroscopy, which is based on the conformal field theory. We extend this method to the multi-degenerated case. As an example, we study the classical 2D 6-clock model which can be mapped to the quantum self-dual 1D 6-clock model. Additionally, we confirm that the self-dual point has a precise numerical agreement with the analytical result, and we argue the degeneracy of the excitation states at the self-dual point from the effective field theoretical point of view.

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“…Besides the operator cos √ 8φ, there are several operators whose scaling dimensions become 2 at the BKT transition point. Recently one of the authors [24] studied the structure of these operators for finite size systems. He found that at the BKT transition point cos √ 8φ and the marginal operator…”

mentioning

confidence: 99%

“…Corresponding eigenvalues are N i=1 S z i , q = 4πn/N , P = ±1 and T = ±1 respectively. The symmetry operations in the sine-Gordon model are as follows [24]. The operation to the space inversion (P ) is φ → −φ,…”

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confidence: 99%

Phase Diagram ofS=1Bond-AlternatingXXZChains

1996

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The phase transitions between the XY, the dimer and the Haldane phases of the spin-1 bond-alternating XXZ chain are studied by the numerical diagonalization. We determine the phase diagram at T = 0 and also identify the universality class with the level spectroscopy. We find that exactly on ∆ = 0 there is a Berezinskii-Kosterlitz-Thouless transition line which separates the XY and the Haldane phase and there exists a multicritical point of the XY, the dimer and the Haldane phases. We discuss that the critical properties of this model is of the 2-D Ashkin-Teller type reflecting the hidden Z2 × Z2 symmetry.Haldane [1] predicted the difference of the critical properties between integer S and half odd integer S spin chains. When S is an integer, the Heisenberg spin chain has a unique disordered ground state with the finite energy gap, while when S is a half odd integer it has no energy gap and belongs to the same universality class as the S = 1/2 case. Den Nijs and Rommelse [2] argued that the Haldane gap system is characterized by the string order parameter which is defined by the non-local operator. Recently the symmetry breaking is recognized as the breakdown of the hidden Z 2 × Z 2 symmetry [3]. In this letter we study the phase diagram of the S = 1 anisotropic spin chain with bond-alternationto see this symmetry breaking. By studying the phase diagram, we show the difference of the topology of the phase diagrams between S = 1 and S = 1/2 cases. First we review the two dimensional (2-D) Ashkin-Teller model which will be useful to understand the model (1). The 2-D Ashkin-Teller model can be thought as two Ising models coupled by a four-spin interaction, and has the Z 2 × Z 2 symmetry. It is known that there is the 2-D Gaussian critical line of 1

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Correlation functions of the 2D sine-Gordon model

Cited by 103 publications

References 54 publications

Ground-state phase diagram ofS=1XXZchains with uniaxial single-ion-type anisotropy

Ground-state phase diagram ofS=1XXZchains with uniaxial single-ion-type anisotropy

Berezinskii–Kosterlitz–Thouless transitions in the six-state clock model

Phase Diagram ofS=1Bond-AlternatingXXZChains

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