Combinatorics of Lax Objects in Bethe Ansatz

R. Stagraczyński Rzeszów University of Technology, The Faculty of Mathematics and Applied Physics, Al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland

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Algebraic Bethe Ansatz, also known as quantum inverse scattering method, is a consistent tool based on the Yang-Baxter equation which allows to construct Bethe Ansatz exact solutions. One of the most important objects in algebraic Bethe Ansatz is a monodromy matrix M̂, which is defined as an appropriate product of so-called Lax operators L̂ (local transition operators). Monodromy matrix as well as each of Lax operators acts in the tensor product of the quantum space ℋ with an auxiliary space ℂ2. Thus M̂, when written in the standard basis of auxiliary space, consists of four elements Â, B̂, Ĉ, D̂, which are the operators acting in quantum space ℋ, where B̂ and Ĉ are step operators and the remaining generate all constants of motion. In this work a consistent method of construction of the Bethe Ansatz eigenstates in terms of objects â, b̂, ĉ, d̂ i.e. matrix elements of the Lax operators in the auxiliary space is proposed.

DOI: 10.12693/APhysPolA.128.216 PACS numbers: 03.65.Aa, 75.10.Jm