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Acta Physica Sinica

SPIN-PEIERLS TRANSITION OF THE ANTIFERROMAGNETIC CHAIN

Zhiguo Wang, Guo-Hui Ding, Xu Bo-wei, 上海交通大学应用物理系，上海 200030

Published Jan 1, 1999• 6 citations
Publisher

Abstract

By using the Fermi-Bose transformation, the antiferromagnetic chain is mapped into the bosonic field, and the energy density of the ground state and the excite states of the model are given. The relationship between the energy density of the ground state and the strength of distortion of the model is obtained. The results show that there exists a spin-Peierls transition in the model. Finally, the numerical simulation is performed to verify the above theoretical prediction.

DOI
10.7498/aps.48.296

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By using the Fermi-Bose transformation, the antiferromagnetic chain is mapped into the bosonic field, and the energy density of the ground state and the excite states of the model are given. The relationship between the energy density of the ground state and the strength of distortion of the model is obtained. The results show that there exists a spin-Peierls transition in the model. Finally, the numerical simulation is performed to verify the above theoretical prediction.
We investigate a one-dimensional S=1S=1S=1 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. Investigating the ground-state energy of the static bond-alternating chain, we find that the instability to a dimerized chain depends on the value of the spin-phonon coupling, unlike the case of S=12.S=\frac{1}{2}.S=21​. The spin state is the dimer state or the uniform Haldane state depending on whether the lattice distorts or not, respectively. At an intermediate value of the spin-phonon coupling, we find the first-order transition between the two states. We also find the coexistence of the two states.
Finite-size scaling calculations for deformable Heisenberg chains with spin value S=(1/2, 1, (3/2, and 2 indicate that as far as the spin-Peierls transition is concerned, the model with any spin S>(1/2 behaves differently from the S=(1/2 situation. For S=(1/2 the ground state of the isotropic antiferromagnetic or planar models is dimerized, irrespective of the strength of the elastic constant. On the other hand, from the extrapolation of finite-chain results it seems that for any higher-spin value the dimerized and uniform phases are separated by a finite critical value of the elastic constant, and the transition is discontinuous.