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Journal of Physics Condensed Matter

Isotropic spin-1 chains with bond alternation: analytic and numerical studies

Kiyohito Totsuka, Yoshihiro Nishiyama, Naomichi Hatano, Masuo Suzuki

Published Jun 19, 1995• 67 citations
Publisher

Abstract

Isotropic spin-1 chains with bond alternation are studied. Analytic (both variational and perturbative) results are presented. A phase transition is found to separate the S=1 Haldane phase and the dimer phase. The critical point is numerically determined using the Binder parameter. The universality class is predicted to be given by the level-1 SU(2) Wess-Zumin-Witten model, and this prediction is supported by the present exact diagonalization study. The dimer phase is found to be connected to the "S=2" Haldane phase in a special limit. The change of the excitation spectra and the string order parameter with bond alternation is discussed.

DOI
10.1088/0953-8984/7/25/014

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Isotropic spin-1 chains with bond alternation are studied. Analytic (both variational and perturbative) results are presented. A phase transition is found to separate the S=1 Haldane phase and the dimer phase. The critical point is numerically determined using the Binder parameter. The universality class is predicted to be given by the level-1 SU(2) Wess-Zumin-Witten model, and this prediction is supported by the present exact diagonalization study. The dimer phase is found to be connected to the "S=2" Haldane phase in a special limit. The change of the excitation spectra and the string order parameter with bond alternation is discussed.
Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian \({\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2\) (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and 0.0≲α≤1.00.0\lesssim\alpha \leq 1.00.0≲α≤1.0.
We discuss spin-SSS antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary SSS. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-2S2S2S SU(2)\mathrm{SU}(2)SU(2) Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of S=1S=1S=1 and S=3/2S=3/2S=3/2 systems by using exact diagonalization and level spectroscopy.
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Crossover and Changeover in Spin-1 Kitaev-ΓΓΓ Chain with Uniaxial Single-ion Anisotropy
Recent advances in bond-directional spin chains have revealed extensive emergent phenomena and unconventional criticality. Here we investigate the spin-1 Kitaev-ΓΓΓ chain with uniaxial single-ion anisotropy (SIA) using large-scale density-matrix renormalization group calculations and bosonization analysis. Tuning the SIA strength reveals a crossover from the Kitaev phase to the large-DDD phase, evidenced by the excitation gap changing from quadratic to linear, the coexistence and smooth evolution of spin-nematic and string order parameters, and the suppression of the double-peak specific heat. For negative SIA, we uncover a changeover from a first-order transition to a continuous one between the dimerized and Haldane phases. The continuous transition belongs to the \textrm{SU(2)2_22​} Wess-Zumino-Witten universality class with central charge c=3/2c=3/2c=3/2, a rare instance in a system without continuous symmetry. Our results establish the Kitaev-ΓΓΓ chain as a minimal platform for controlling crossover and changeover phenomena.
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The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Néel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Néel and dimer-Néel). We determine the phase boundary and universality class using the recent developed techniques by the authors.