Numerical Study of the<i>S</i>=1 Antiferromagnetic Spin Chain with Bond Alternation

Kato, Yusuke; Tanaka, Akihiro

doi:10.1143/jpsj.63.1277

Cited by 128 publications

(111 citation statements)

References 35 publications

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“…Further, the number of gapless points is predicted to be the number of integers ≤ S + 1/2; in particular, the undimerized chain (with κ = 1) is a gapless point if S is a half-odd-integer. Numerical analysis shows this to be true for values of S up to 2 [8,9,10,11]; however, the numerically obtained values of κ at the gapless points do not agree well with the NLSM values. It therefore appears that there must be corrections to the NLSM analysis for small values of S.…”

Section: Introductionmentioning

confidence: 74%

Gapless points of dimerized quantum spin chains: Analytical and numerical studies

2006

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We study the locations of the gapless points which occur for quantum spin chains of finite length (with a twisted boundary condition) at particular values of the nearest neighbor dimerization, as a function of the spin S and the number of sites. For strong dimerization and large values of S, a tunneling calculation reproduces the same results as those obtained from more involved field theoretic methods using the non-linear σ-model approach. A different analytical calculation of the matrix element between the two Néel states gives a set of gapless points; for strong dimerization, these differ significantly from the tunneling values. Finally, the exact diagonalization method for a finite number of sites yields a set of gapless points which are in good agreement with the Néel state calculations for all values of the dimerization, but the agreement with the tunneling values is not very good even for large S. This raises questions about possible corrections to the tunneling results.

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Section: Introductionmentioning

confidence: 74%

Gapless points of dimerized quantum spin chains: Analytical and numerical studies

2006

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“…Their argument was successfully confirmed by several theoretical methods [16,17,18,19,20,21,22,23,24]. For the S = 1 system, the critical α separating the Haldane phase (α c < α < 1) and the singlet-dimer phase (0 < α < α c ) was estimated using a series expansion method [16], a density-matrix renormalizationgroup method [17], quantum Monte Carlo methods [18,19,23,24], the Binder parameter combined with finitesize scaling [20], and a level-crossing method [22].…”

Section: Introductionmentioning

confidence: 81%

“…At α = 0.6, the system is in the vicinity of the gapless point [16,17,18,19,20,22,23,24]. The residues in 0 < q ≤ π decrease with increasing N , indicating that the lowest excited states in 0 ≤ q ≤ π form the lower edge of the excitation continuum.…”

Section: A Haldane Phasementioning

confidence: 99%

Dynamical structure factors ofS=1bond-alternating Heisenberg chains

Suzuki

Suga

2003

Phys. Rev. B

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We calculate the dynamical structural factor of the S = 1 bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in 0 ≤ q ≤ qc and the one-magnon mode in qc ≤ q ≤ π. As the system approaches the gapless point, qc shifts towards q = π and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in 0 ≤ q ≤ qc. As the bond-alternation becomes strong, qc shifts towards q = π. In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in 0 ≤ q ≤ 0.2π and 0.8π ≤ q ≤ π, and the one-magnon mode appears in 0.2π < q < 0.8π. The largest integrated intensity of the one-magnon mode is 93%, which is slightly smaller than that in the S = 1 Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.

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“…This equation gives the single gapless point J 2 /J 1 = 1(l = 1) for s = 1/2 and J 2 /J 1 = 1/3(l = 1) for s = 1. Numerical calculations for s = 1 show that the gapless point is at J 2 /J 1 = 0.6 [9,10] and an experiment for [{Ni(333-tet)(µ-N 3 )} n ](ClO 4 ) n agrees with this value [11]. Hence the method of the NLSM does not always give quantitatively correct results.…”

Section: (Recieved)mentioning

confidence: 94%

NonlinearσModel for Inhomogeneous Spin Chains

Takano

1999

Phys. Rev. Lett.

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We derive a non-linear σ model (NLSM) generally representing antiferromagnetic Heisenberg spin chains with inhomogeneous spin magnitudes and inhomogeneous nearest-neighbor exchange constants arrayed in finite periods. Only a restriction is that the average of spin magnitudes on one sublattice is the same as that on the other sublattice. The NLSM gives the gapless condition explicitly written by the spin magnitudes and the exchange constants. We apply this gapless condition to several cases including systems with impurities.PACS numbers: 75.10. Jm, 75.30.Et, 75.30.Hx In 1983 Haldane predicted that an antiferromagnetic Heisenberg spin chain is gapful if the spin magnitude is an integer, and is gapless if it is a half-odd-integer [1]. Since his theory is based on mapping of a spin model to the non-linear σ model (NLSM), the usefulness of the NLSM is recognized by researchers in condensed matter physics. Various interesting aspects of the method of the NLSM are mentioned in some books [2,3,4]. Extension of the NLSM method to systems with inhomogeneity in spins and exchange constants is a challenging problem. It is not only theoretically important but also useful in explaining and suggesting experiments. Affleck reformulated the NLSM method and applied to a spin chain with bond alternation [5]. He divided the spin chain into blocks each of which contains two spins, and defined new variables for each block. Affleck and Haldane analyzed and predicted gapless points for general homogeneous spin chains [6]. Fukui and Kawakami tried to extend the NLSM method to a spin chain including impurities and to spin chains with unit cell containing three and four spins [7,8]. They rather intuitively introduced new variables to form an NLSM and did not care to preserve the degrees of freedom. Hence we cannot determine whether their resultant NLSM's are correct or not by inspecting their theory itself.In this Letter, we obtain a NLSM generally representing a wide class of inhomogeneous antiferromagnetic spin chains. The derivation is based on the idea dividing the system into blocks [5] but blocks used here are generally defined to contain more than two spins. In a path integral formula, the variables of integration for each block are transformed to form the NLSM with preserving the original degrees of freedom. We apply this NLSM to several cases including systems with impurities and examine gapless conditions.We consider the spin chain represented by the Hamiltonianwhere S j is the spin at site j and J j (> 0) is the exchange constant between S j and S j+1 . The number of lattice sites is N , the lattice spacing is a and the system size is L = aN . The quantum number for the magnitude of S j is denoted by s j . The system is periodic with period 2b (b: a positive integer):We divide the spin chain into blocks each of which contains 2b spin sites. The block size 2ba is a positive integer (even number) times the size of the unit cell if a unit cell contains an even (odd) number of spins. In a block {J j } and {s j } are arbitrary ex...

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Numerical Study of theS=1 Antiferromagnetic Spin Chain with Bond Alternation

Cited by 128 publications

References 35 publications

Gapless points of dimerized quantum spin chains: Analytical and numerical studies

Gapless points of dimerized quantum spin chains: Analytical and numerical studies

Dynamical structure factors ofS=1bond-alternating Heisenberg chains

NonlinearσModel for Inhomogeneous Spin Chains

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