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Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

by J. M. Maillet, G. Niccoli, B. Pezelier

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Submission summary

Authors (as registered SciPost users): Jean Michel Maillet · Giuliano Niccoli
Submission information
Preprint Link:  (pdf)
Date accepted: 2017-02-24
Date submitted: 2017-02-21 01:00
Submitted by: Maillet, Jean Michel
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the lattice sine-Gordon model with integrable open boundary conditions. This spectral analysis is developed by implementing the method of separation of variables (SoV). The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions. Moreover, we prove an equivalent characterization as the set of solutions to a Baxter's like T-Q functional equation and rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form. In order to explain our method in a simple case, the present paper is restricted to representations containing one constraint on the boundary parameters and on the parameters of the Bazhanov-Stroganov Lax operator. In a next article, some more technical tools (like Baxter's gauge transformations) will be introduced to extend our approach to general integrable boundary conditions.

Author comments upon resubmission

This is the new version of our article including changes according to the referees reports and our replies to these reports.

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Published as SciPost Phys. 2, 009 (2017)

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