Direct diagonalisation of the Heisenberg Hamiltonian for a magnetic ring within the two-deviation sector by means of the Chebyshev polynomials
type: Item
instance of: scholarly article
title: Direct diagonalisation of the Heisenberg Hamiltonian for a magnetic ring within the two-deviation sector by means of the Chebyshev polynomials
zbMATH Open document ID: 1275.82004
DOI: 10.1016/S0034-4877(12)60050-0
author: Jan Milewski
published in: Reports on Mathematical Physics
publication date: 2013-03-14T00:00:00Z
review text: 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.
reviewed by: Farruh Mukhamedov
Mathematics Subject Classification ID: 82B23
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 6145028
zbMATH Keywords: Heisenberg ring
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Bethe parameters
MaRDI profile type: Publication
cites work: Q4747353
cites work: Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
cites work: Q4791752
description: scientific article; zbMATH DE number 6145028