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Calculation of norms of Bethe wave functions. (English) Zbl 0531.60096

The Bethe approach has been used successfully to solve many two dimensional models in quantum statistical mechanics. Recently these solutions have been investigated using the newly developed method of quantum inverse scattering (for systems in a finite box) yielding the results that the norms of these eigenfunctions of the Hamiltonian are equal to some Jacobians [see M. Gaudin, B. M. McCoy, and T. T. Wu, Normalization sum for the Bethe’s hypothesis wave functions of the Heisenberg-Ising chain. Phys. Rev. D 23, 417-419 (1981)]. The author has supplied the proof of this conjecture for a class of models. The main corpus of the paper consists of a generalization of this to cover a six vertex model necessitating the consideration of an inhomogeneous monodromy matrix. Some models like the quantum nonlinear Schrödinger equation are also treated as illustrations.
Reviewer: Y.Prahalad

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B10 Quantum equilibrium statistical mechanics (general)
82B26 Phase transitions (general) in equilibrium statistical mechanics
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