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arXiv:cond-mat/9907134 · Journal of Physics A Mathematical and General

Exactly solvable quantum spin tubes and ladders

Murray T. Batchelor, M. Maslen

Published Aug 11, 1999• 40 citations
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Abstract

We find families of integrable n -leg spin-½ ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su ( N ) spin chains with N = 2 n . Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are n -dependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe ansatze.

DOI
10.1088/0305-4470/32/33/102

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We find families of integrable n -leg spin-½ ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su ( N ) spin chains with N = 2 n . Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are n -dependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe ansatze.
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.