Ground State Phase Diagram of the One DimensionalS=1/2XXZ Model with Dimerization and Quadrumerization

Chen, Wei; Hida, Kazuo

doi:10.1143/jpsj.68.2779

Cited by 5 publications

(3 citation statements)

References 19 publications

(27 reference statements)

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“…The results of this work are compared with our previous work 15) on the one dimensional S = 1/2 XXZ model with dimerization 1 − j and quadrumerization δ. The Hamiltonian is given by…”

Section: Limit §3 Summary and Discussionmentioning

confidence: 97%

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

2000

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One dimensional S = 1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D ≥ 0. The ground states of this model contain the Haldane state, large-D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.KEYWORDS: Heisenberg chain, exact diagonalization, conformal field theory, dimer phase, Haldane phase, large-D phase §1. IntroductionOne dimensional antiferromagnetic Heisenberg chains have been the subject of recent investigations by numerous groups. The various phenomena of current interest are shown to be due to quantum effects. A uniform antiferromagnetic Heisenberg chain is known to have a gapless ground state for half-integer-spin. Especially, the exact solution is available for S = 1/2 chain.1) In contrast, for the integer-spin,2) there is a gap between the first excited state and ground state.One dimensional S = 1 antiferromagnetic Heisenberg chains with bond alternation undergo a transition from the Haldane state to the dimer state as the strength of bond alternation increases. This transition has been studied by many methods.3-5) On the other hand, the phase boundaries and critical properties of S = 1 Heisenberg chains with uniaxial single-ion anisotropy 6) were determined by Glaus and Schneider using a finite size scaling method. The physical picture of both states was clarified by Nijs and Rommelse in terms of string order 7) and by Tasaki using a stochastic geometric representation.8) Using an exact diagonalization method and a phenomenological renormalization group approach, Tonegawa et al. calculated the phase diagram of the S = 1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy. They found the Haldane phase, Néel phase, dimer phase and large-D phase in the ground state. No phase transition was found, however, between the dimer phase and large-D phase.9) In this paper, we calculate the ground state phase diagram of a one demensional S = 1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy using the twisted boundary condition method.5, 10) This improves the accuracy of the transition points. Using conformal field theory and the level spectroscopy method, we obtain the * E-mail: chenwei@riron.ged.saitama-u.ac.jpLuttinger liquid parameter K and the critical exponent ν of the energy gap.This paper is organized as follows. In the next section, the model Hamiltonian is defined and the numerical results are presented. From the exact diagonalization data with the twisted boundary condition, the ground state phase diagram is obtained. The Luttinger liquid parameter K is calculated by conformal field theory and the level spectroscopy method at the transition p...

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“…The results of this work are compared with our previous work 15) on the one dimensional S = 1/2 XXZ model with dimerization 1 − j and quadrumerization δ. The Hamiltonian is given by…”

Section: Limit §3 Summary and Discussionmentioning

confidence: 97%

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

2000

Self Cite

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“…And it is being recognized as powerful in investigations of 1D electron systems 17,18,22,23 as well as quantum spin chains. [24][25][26] Following these developments, the present author has recently investigated many-body effects of spin-dependent non-point-like Coulomb interactions through the 1D halffilled ''anisotropic'' extended Hubbard model ͑AEHM͒ defined by the Hamiltonian: H AEHM ϭH HM ϩH AE with in the repulsive case (U, V 1,2 Ͼ0). 27 There we parametrized spin-dependent Coulomb interactions as V 1,2 ϭV(1ϯ␦) ͑the upper sign refers to the former in such expressions͒.…”

Section: Introductionmentioning

confidence: 99%

Global structure of ground-state phase diagrams in the one-dimensional anisotropic extended Hubbard model

Otsuka¹

2001

Phys. Rev. B

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We discuss global structures of ground-state phase diagrams in a one-dimensional half-filled electron system with on-site and spin-dependent nearest-neighbor-site Coulomb interactions. We compare our numerical calculation data for phase boundary lines with their analytical expressions in three limiting regions of interaction parameters and find good agreement between them. In the intermediate-coupling region, however, we observe nontrivial structures of phase diagrams: For systems with weak easy-plain anisotropy, both the bond-located spin-and charge-density-wave phases are realized. The latter contacts with the ferromagnetic phase stabilized in the strong-coupling region. On the other hand, when anisotropy becomes large, the intermediate phase disappears and consequently a direct transition between the former and ferromagnetic phase is observed.

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“…3(b), the Haldane phase and the dimer phase are separated by a critical phase transition. In the Hermitian case (D = B x = 0), it is known that the criticality is described by a conformal field theory with central charge c = 1 [47,48]. For a one-dimensional critical system of length N 1 with PBC, let A be a segment (subsystem) of length r and B be the rest of the system.…”

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confidence: 99%

Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems

Tsubota,

Yang,

Akagi

et al. 2021

Preprint

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We investigate the quantization of the complex-valued Berry phase in non-Hermitian quantum systems with certain generalized symmetries. In Hermitian quantum systems, the real-valued Berry phase is known to be quantized in the presence of certain symmetries, and this quantized Berry phase can be regarded as a topological order parameter for gapped quantum systems. In this paper, on the other hand, we establish that the complex Berry phase is also quantized in the systems described by a family of non-Hermitian Hamiltonians. Let H(θ) be a non-Hermitian Hamiltonian parameterized by θ. Suppose that there exists a unitary and Hermitian operator P such that P H(θ)P = H(−θ) or P H(θ)P = H † (−θ). We prove that in the former case, the complex Berry phase γ is Z2-quantized, while in the latter, only the real part of γ is Z2-quantized. The operator P can be viewed as a generalized symmetry for H(θ), and in practice, P can be, for example, a spatial inversion. We also argue that this quantized complex Berry phase is capable of classifying non-Hermitian topological phases, and we demonstrate this in some one-dimensional strongly correlated systems.

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Ground State Phase Diagram of the One DimensionalS=1/2XXZ Model with Dimerization and Quadrumerization

Cited by 5 publications

References 19 publications

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

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

Global structure of ground-state phase diagrams in the one-dimensional anisotropic extended Hubbard model

Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems

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