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arXiv:cond-mat/9808300 · Journal of the Physical Society of Japan

Magnetization Plateaus in One DimensionalS=1/2Heisenberg Model with Dimerization and Quadrumerization

Wei Chen, Kazuo Hida, Hiroki Nakano

Published Feb 15, 1999• 20 citations
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Abstract

The one dimensional $S=1/2$ Heisenberg model with dimerization ($1-j$) and quadrumerization ($δ$) in the magnetic field is studied by means of the numerical exact diagonalization of finite size systems and the conformal field theory. It is found that the magnetization plateau at half of the saturation value exists for $δ\neq 0$. For $δ= 0$, this model is described by the conformal field theory with central charge $c=1$ at this value of magnetization. The critical exponent $ν$ which characterizes the $δ$-dependence of the width of the plateau is calculated using the level spectroscopy method. The $j$-dependence of the critical exponent $ν$ is found to be non-monotonic and discontinuous at $j = 0$. The effective theory of the magnetization plateau is also presented for various limiting cases.

DOI
10.1143/jpsj.68.625

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We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field h3{h}_{3}h3​ and a dimer field with period q and strength $\ensuremath{\delta}$. The latter generates a magnetization plateau at $M=(1\ensuremath{-}q/\ensuremath{\pi})/2$, which evolves with strength $\ensuremath{\delta}$ of the perturbation as ${\ensuremath{\delta}}^{\ensuremath{\epsilon}}$, where $\ensuremath{\epsilon}=\ensuremath{\epsilon}{(h}_{3},\ensuremath{\alpha})$ is related to the $\ensuremath{\eta}$ exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched off $(\ensuremath{\delta}=0)$. We also discuss the appearance of magnetization plateaus in ladder systems with l legs.
We investigate the S=2S=2S=2 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.
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