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arXiv · 1401.4901

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV

N. Kitanine·J. -M. Maillet·G. Niccoli
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Abstract

We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to be equivalent to the known separation of variable (SOV) representation hence proving that it defines a complete characterization of the transfer matrix spectrum. The polynomial character of the Q-function allows us then to show that a finite system of equations of generalized Bethe type can be similarly used to describe the complete transfer matrix spectrum.

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N. Kitanine, J. -M. Maillet, G. Niccoli. 2014-01-20. Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV. https://doi.org/10.1088/1742-5468%2F2014%2F05%2Fp05015

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