Norms of bound states
type: Item
instance of: scholarly article
title: Norms of bound states
zbMATH Open document ID: 0637.47004
DOI: 10.1007/BF01084936
published in: Journal of Soviet Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The quantum inverse scattering method is a procedure for constructing the eigenfunctions for quantum chain Hamiltonians by means of an algebraic ``Bethe ansatz''. The norms of these eigenfunctions enter into the calculation of correlation functions for the lattice models associated with the Hamiltonian (which is related to its transfer matrix). The application of this procedure to the XXX and XXY Heisenberg chains is reviewed in this paper and aspects of the bound states of various numbers of elementary excitations are discussed. The principal content of this article is the derivation of an expression for the norm of the bound state wave functions in terms of certain Jacobian determinants arising in the Bethe ansatz algebra.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81T25
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 4038560
zbMATH Keywords: quantum inverse scattering method
zbMATH Keywords: eigenfunctions for quantum chain Hamiltonians
zbMATH Keywords: calculation of correlation functions
zbMATH Keywords: bound states
zbMATH Keywords: expression for the norm of the bound state wave functions
zbMATH Keywords: terms of certain Jacobian determinants arising in the Bethe ansatz algebra
author: Anatol N. Kirillov
author: Vladimir E. Korepin
MaRDI profile type: Publication
cites work: Calculation of norms of Bethe wave functions
cites work: The quantum inverse scattering method approach to correlation functions.
cites work: Correlation functions of the one-dimensional Bose gas in the repulsive case.
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description: scientific article; zbMATH DE number 4038560