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Workshop on Integrable Theories, Solitons and Duality

Integrable spin ladder systems

Angela Foerster, Arlei Prestes Tonel

Published Dec 1, 2002• 0 citations
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Abstract

We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings.The model is exactly solvable by means of the Bethe ansatz method.We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram.Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters.We also investigate the thermodynamics of the model.Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically.The influence of this anisotropy parameter on these physical curves is determined explicitly.A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.

DOI
10.22323/1.008.0013

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We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings.The model is exactly solvable by means of the Bethe ansatz method.We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram.Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters.We also investigate the thermodynamics of the model.Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically.The influence of this anisotropy parameter on these physical curves is determined explicitly.A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.
We investigate the thermodynamics of an integrable spin ladder model which possesses a free parameter besides rung and leg couplings. The model is exactly solvable by means of the Bethe ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. The spin gap obtained from the susceptibility curve and the one obtained from the Bethe ansatz equations are in very good agreement. Our results for the magnetic susceptibility fit well the experimental data for the organometallic compounds (5IAP) 2 CuBr 4 ·2H 2 O (Landee C. P. et al. , Phys. Rev. B , 63 (2001) 100402(R)) Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 (Hayward C. A., Poilblanc D. and Lèvy L. P., Phys. Rev. B , 54 (1996) R12649, Chaboussant G. et al. , Phys. Rev. Lett. , 19 (1997) 925; Phys. Rev. B , 55 (1997) 3046.) and (C 5 H 12 N) 2 CuBr 4 (Watson B. C. et al. , Phys. Rev. Lett. , 86 (2001) 5168) in the strong-coupling regime.
We present an integrable spin-ladder model, which possesses a free parameter besides the rung coupling J. Wang's system based on the SU(4)\mathrm{SU}(4)SU(4) symmetry can be obtained as a special case. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with three free parameters.
Two integrable spin ladder systems with different types of impurities are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly and the Bethe ansatz equations as well as the energy eigenvalues are obtained. We show for both models that a phase transition between gapped and gapless spin excitations occurs at a critical value of the rung coupling J. In addition, the dependence of the impurities on this phase transition is determined explicitly. Remarkably, in one of the models a decreasing of the spin gap with increasing impurity strength is found.