Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables - Archive ouverte HAL
Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2014

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

Jean Michel Maillet
G. Niccoli

Résumé

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.

Dates et versions

hal-02324545 , version 1 (21-10-2019)

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Citer

N. Kitanine, Jean Michel Maillet, G. Niccoli. Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables. Journal of Statistical Mechanics: Theory and Experiment, 2014, 2014 (5), pp.P05015. ⟨10.1088/1742-5468/2014/05/P05015⟩. ⟨hal-02324545⟩
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