Analytical and combinatorial aspects of the eigenproblem for the two-magnon sector of XXX Heisenberg rings
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In this paper we study both analytical and combinatorial properties of solutions of the
eigenproblem for the Heisenberg s-1/2 model for two deviations. Our analysis uses Chebyshev
polynomials, inverse Bethe Ansatz, winding numbers and rigged string configurations. We show some combinatorial aspects of strings in a geometric way. We discuss some exceptions from the connection between the combinatorial nature of an eigenstate and the analytical type of a solution of the eigenproblem. In particular, as an illustration of the aforementioned exceptions, we analyze the singularities of Bethe parameters for bound states at the border of the Brillouin zone.
eigenproblem for the Heisenberg s-1/2 model for two deviations. Our analysis uses Chebyshev
polynomials, inverse Bethe Ansatz, winding numbers and rigged string configurations. We show some combinatorial aspects of strings in a geometric way. We discuss some exceptions from the connection between the combinatorial nature of an eigenstate and the analytical type of a solution of the eigenproblem. In particular, as an illustration of the aforementioned exceptions, we analyze the singularities of Bethe parameters for bound states at the border of the Brillouin zone.