Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

Abstract

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.

15 pages, standard LaTeX

References in corpus (3)

• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Algebraic Structures Related to Reflection Equations
• Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem

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• From affine Hecke algebras to boundary symmetries
• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
• The open XXZ and associated models at q root of unity
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• A note on the boundary spin $s$ XXZ chain
• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model