Critical Properties of Spin-1 Antiferromagnetic Heisenberg Chains with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Chen, Wei; Hida, Kazuo; Sanctuary, B. C.

doi:10.1143/jpsj.69.237

Cited by 28 publications

(30 citation statements)

References 16 publications

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“…We illustrate our results in Fig. 6 together with those of previous reports [9,11,25]. Our estimates of D : evaluated value of x-component, ♦: evaluated value of z-component, +: Ref.…”

Section: B Haldane-large-d Transition Linementioning

confidence: 51%

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Finite-size scaling of string order parameters characterizing the Haldane phase

2008

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We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi-point correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S = 1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density matrix renormalization group method. We focus on the gradient of the inversedsystem-size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method to directly observe quantum phase transitions.

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“…We illustrate our results in Fig. 6 together with those of previous reports [9,11,25]. Our estimates of D : evaluated value of x-component, ♦: evaluated value of z-component, +: Ref.…”

Section: B Haldane-large-d Transition Linementioning

confidence: 51%

“…[11], △: Ref. [25]. The inset of (b) magnifies the data at Jz = 1 to allow a clear comparison to distinguish the data.…”

Section: B Haldane-large-d Transition Linementioning

confidence: 99%

Finite-size scaling of string order parameters characterizing the Haldane phase

2008

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“…Here, we give two examples for such a situation. One is an antiferromagnetic S = 1 chain with the bond alternation and the on-site anisotropy, 17,18) in which the LD state and the dimer state belong to the same phase. The other is an antiferromagnetic S = 1 two-leg ladder, 19) where the Haldane state and the rung-dimer state belong to the same phase called the four-site plaquette singlet phase.…”

Section: )mentioning

confidence: 99%

Haldane, Large-D, and Intermediate-DStates in anS= 2 Quantum Spin Chain with On-Site andXXZAnisotropies

et al. 2011

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Using mainly numerical methods, we investigate the ground-state phase diagram of the S = 2 quantum spin chain described by H = j (S Quantum spin chain systems have been attracting increasing attention in recent years because they provide rich physics even when models are rather simple. The most well-known example may be the existence of the Haldane phase 1, 2) in integer spin chain systems only with isotropic nearest-neighbor (nn) interactions.In this study, using mainly numerical methods, we explore the ground-state phase diagram of the S = 2 quantum spin chain described by the Hamiltonianwhere S α j (α = x, y, z) is the α-component of the S = 2 operator at the j-th site, and ∆ and D are, respectively, the XXZ anisotropy parameter of the nn interactions and the on-site anisotropy parameter. Hereafter, we denote the total number of spins in the system by N , assumed to be even, and the z component of the total spin by M = j S z j . The ground-state phase diagram on the ∆-D plane of the same Hamiltonian in the S = 1 case was discussed by Schulz 3) and den Nijs and Rommels, 4) and numerically determined by Chen et al. 5) In the present S = 2 case, Schulz 3) discussed the ground-state phase diagram with six phases obtained by the bosonization method; the phases are, in our terminology, the ferromagnetic (FM) phase, the Néel phase, the XY 1 phase, the XY 4 phase, the Haldane phase and the large-D (LD) phase. The XY 1 state is characterized by the power decay of * E-mail address: tone0115@vivid.ocn.ne.jp Figs. 1(a) and (c), respectively. About twenty years ago, Oshikawa 6) predicted, in S ≥ 2 integer quantum spin cases, the existence of the intermediate-D (ID) phase, the valence bond picture of which is depicted in Fig. 1(b). Figure 2(a) is an interpretation of Oshikawa's prediction by Aschauer and Schollwöck 7) in the S = 2 case. On the other hand, carrying out the density-matrix renormalization-group (DMRG) calculation, Schollwöck et al. 8,9) and Aschauer and Schollwöck 7) proposed the phase diagram in Fig. 2(b) and concluded the absence of

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“…For the purpose of exploring the effect of frustration, we are now studying the case where the antiferromagnetic next-nearest-neighbor interaction term J 2 S · S +2 (J 2 > 0) is added to the Hamiltonian of eqs. (1-3), assuming either J > 0 or J < 0.…”

Section: Discussionmentioning

confidence: 99%

“…1,2) As for the zero-field properties, the ground-state phase diagram on the J versus D plane, in which the Néel, Haldane, large-D, and dimer phases appear, has been determined. 1,2) On the other hand, the results for the ground-state magnetization curve show that the magnetization plateau at a half of the saturation magnetization, which is called the …”

Section: Introductionmentioning

confidence: 99%

Finite-Field Ground State of theS=1 Antiferromagnetic–Ferromagnetic Bond-Alternating Chain

2005

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We investigate the finite-field ground state of the S = 1 antiferromagnetic-ferromagnetic bond-alternating chain described by the Hamiltonian H = È ¨where J ≤ 0 and −∞ < D < ∞. We find that two kinds of magnetization plateaux at a half of the saturation magnetization, the 1 2 -plateaux, appear in the ground-state magnetization curve; one of them is of the Haldane type and the other is of the large-D-type. We determine the 1 2 -plateau phase diagram on the D versus J plane, applying the twistedboundary-condition level spectroscopy methods developed by Kitazawa and Nomura. We also calculate the ground-state magnetization curves and the magnetization phase diagrams by means of the density-matrix renormalization-group method.KEYWORDS: S = 1 antiferromagnetic-ferromagnetic bond-alternating chain, numerical methods, groundstate magnetization curve, -plateau phase diagram, magnetization phase diagram

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Critical Properties of Spin-1 Antiferromagnetic Heisenberg Chains with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Cited by 28 publications

References 16 publications

Finite-size scaling of string order parameters characterizing the Haldane phase

Finite-size scaling of string order parameters characterizing the Haldane phase

Haldane, Large-D, and Intermediate-DStates in anS= 2 Quantum Spin Chain with On-Site andXXZAnisotropies

Finite-Field Ground State of theS=1 Antiferromagnetic–Ferromagnetic Bond-Alternating Chain

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