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An explicit demonstration of integrability for the linear Heisenberg chain of N = 9 nodes
Author(s) -
Topolewicz Stanislaw,
Lulek Tadeusz
Publication year - 2007
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200674624
Subject(s) - bethe ansatz , eigenvalues and eigenvectors , hamiltonian (control theory) , chain (unit) , mathematical physics , spectrum (functional analysis) , mathematics , physics , string (physics) , combinatorics , quantum mechanics , integrable system , mathematical optimization
We propose the system of N – 1 = 8 mutually commuting operators which classify all eigenstates of the Heisenberg Hamiltonian for the linear magnetic chain of N = 9 nodes, each with the spin 1/2. These eigenstates, determined exactly by Bethe Ansatz and classified combinatorially by rigged string configurations of Kerov, Kirillov and Reshetikhin, can be also associated with the spectrum of this set of commuting operators. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)