Bethe Ansatz and Classical Hirota Equation
نویسندگان
چکیده
منابع مشابه
Hirota Equation and Bethe Ansatz
The paper is a review of recent works devoted to analysis of classical integrable structures in quantum integrable models solved by one or another version of the Bethe ansatz. Similarities between elements of the quantum and classical theories of integrable systems are discussed. Some key notions of the quantum theory, now standard in the quantum inverse scattering method, are identiied with ty...
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A brief non-technical review of the recent study [1] of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's Q-operators, etc) with elements of classical non-linear integrable difference equations (τ-functions, Baker-Akhiezer functions, etc). The nested Bethe ansatz...
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We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic...
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We consider GL(K|M)-invariant integrable supersymmetric spin chains with twisted boundary conditions and elucidate the role of Bäcklund transformations in solving the difference Hirota equation for eigenvalues of their transfer matrices. The nested Bethe ansatz technique is shown to be equivalent to a chain of successive Bäcklund transformations " undressing " the original problem to a trivial ...
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We study the Pöschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms of the Heun function. At particular values there is a interesting interpretation in terms of finite lattice spin2 XXZ quantum chain with ∆ = cos π L (for free...
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ژورنال
عنوان ژورنال: International Journal of Modern Physics B
سال: 1997
ISSN: 0217-9792,1793-6578
DOI: 10.1142/s0217979297000101