Direct diagonalisation of the Heisenberg Hamiltonian for a magnetic ring within the two-deviation sector by means of the Chebyshev polynomials
The paper is devoted to an exact form of the solution of the original Heisenberg eigenproblem for the case \(r=2\) spin deviations. Note that originally such a problem was solved by the Bethe anzatz, where it was used the hypothesis of strings. In the present paper, the author derives the same solution without mentioned hypothesis. It established that a Hamiltonian block, corresponding to a definite quasi-momentum \(k\), has a three-diagonal form in the wavelet basis. This yields that its characteristic polynomial can be expressed in terms of Chebyshev polynomials. Moreover, a comparison with the solution using the Bethe ansatz is given, which consists in an ex post derivation of the original Bethe parameters (pseudomomenta, spectral parameters, etc.) from known quasi-momentum and energy.
scientific article; zbMATH DE number 6145028