Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End

Abstract

In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid (SOS) model with one reflecting end and domain wall boundary conditions. We show that these two problems are related through a gauge transformation (so-called vertex-face transformation) and can be solved using the same dynamical reflection algebras.

based on a talk given at RAQIS'10, Recent Advances in Quantum Integrable Systems, Annecy-le-Vieux, France, 15-18 June 2010

References in corpus (7)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Correlation functions of the open XXZ chain I
• Correlation functions of the open XXZ chain II
• SOS model partition function and the elliptic weight functions
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms

Cited by in corpus (23)

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• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
• Multiple integral representation for the trigonometric SOS model with domain wall boundaries
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Koornwinder polynomials and the XXZ spin chain
• On Separation of Variables for Reflection Algebras
• Boundary quantum Knizhnik-Zamolodchikov equations and fusion
• Scalar products of the open XYZ chain with non-diagonal boundary terms
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• The deformed Inozemtsev spin chain
• Connection problems for quantum affine KZ equations and integrable lattice models
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model