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A convenient basis for the Izergin-Korepin model. (English) Zbl 1404.82023
Summary: We propose a convenient orthogonal basis of the Hilbert space for the quantum spin chain associated with the \(A_2^{(2)}\) algebra (or the Izergin-Korepin model). It is shown that compared with the original basis the monodromy-matrix elements acting on this basis take relatively simple forms, which is quite similar as that for the quantum spin chain associated with \(A_n\) algebra in the so-called F-basis. As an application of our general results, we present the explicit recursive expressions of the Bethe states in this basis for the Izergin-Korepin model.
MSC:
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
17B81 Applications of Lie (super)algebras to physics, etc.
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
82B23 Exactly solvable models; Bethe ansatz
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