Abstract
We propose a convenient orthogonal basis of the Hilbert space for the quantum spin chain associated with the A2(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 An 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.
Highlights
The quantum inverse scattering method (QISM) (or the algebraic Bethe Ansatz method (ABA)) provides a powerful method of solving eigenvalue problems for quantum integrable systems [1]
It was shown [3] that for the inhomogeneous XXX and XXZ spin chains there does exist a particular basis, in which the actions of the monodromy matrices can be simplified dramatically. This leads to the analysis of these models in the F-basis [5]. Since such a basis has been constructed for other models only related to the A-type algebras: the high-spin XXX spin chains [6], the quantum integrable spin chains [7] associated with gl(m) algebra and their elliptic generalizations [8, 9], and the supersymmetric Fermionic models related to the superalgebras gl(m|n) [10, 11]
The states given by (3.11) (resp. (3.12)) are eigenstates of the commutative family A1(u) and serve as the basis of the left Hilbert space for generic inhomogeneous parameters {θj}. These kind of states are relevant to the separation of variables (SoV) [24] states and the F-basis [3] for the quantum spin chain associated with the A-type algebra
Summary
The quantum inverse scattering method (QISM) (or the algebraic Bethe Ansatz method (ABA)) provides a powerful method of solving eigenvalue problems for quantum integrable systems [1]. In this framework, the quasi-particle creation and annihilation operators are constructed by the off-diagonal matrix elements of the monodromy-matrix. The purpose of the present paper is to propose a representation basis for the IK model with periodic boundary condition, which would play a similar role as that of the F-basis for quantum integrable systems related to the A-type. Some detailed technical calculations are given in Appendices A-C
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
