Quantum inverse scattering method and algebraized matrix Bethe-Ansatz

Takashi Takebe

The quantum inverse scattering method is applied to the inhomogeneous Heisenberg XYZ model with general spins, i.e. the general spin representations of the Sklyanin algebra. By means of the generalized Bethe ansatz developed by Takhtajan and Faddeev (1979) the eigenvectors and eigenvalues of the transfer matrix are found.

P. P. Kulish

Ryszard Stagraczyński

Algebraic Bethe Ansatz, also known as quantum inverse scattering method, is a consistent tool based on the YangBaxter equation which allows to construct Bethe Ansatz exact solutions.One of the most important objects in algebraic Bethe Ansatz is a monodromy matrix M , which is dened as an appropriate product of so-called Lax operators L (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 C 2 .Thus M , when written in the standard basis of auxiliary space, consists of four elements A, B, C, D, which are the operators acting in quantum space H, where B and C 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 a, b, c, d i.e. matrix elements of the Lax operators in the auxiliary space is proposed.

Ryszard Stagraczyński

Algebraic Bethe Ansatz, also known as quantum inverse scattering method, is a consistent tool based on the YangBaxter equation which allows to construct Bethe Ansatz exact solutions.One of the most important objects in algebraic Bethe Ansatz is a monodromy matrix M , which is dened as an appropriate product of so-called Lax operators L (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 C 2 .Thus M , when written in the standard basis of auxiliary space, consists of four elements A, B, C, D, which are the operators acting in quantum space H, where B and C 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 a, b, c, d i.e. matrix elements of the Lax operators in the auxiliary space is proposed.

Miki Wadati