Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 054, 18 pages      arXiv:1804.00597

Modified Algebraic Bethe Ansatz: Twisted XXX Case

Samuel Belliard ab, Nikita A. Slavnov c and Benoit Vallet b
a) Sorbonne Université, CNRS, Laboratoire de Physique Théorique et Hautes Energies, LPTHE, F-75005, Paris, France
b) Institut de Physique Théorique, DSM, CEA, URA2306 CNRS Saclay, F-91191, Gif-sur-Yvette, France
c) Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Received April 09, 2018, in final form May 28, 2018; Published online June 07, 2018

We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two basis to characterize the spectral problem and two families of inhomogeneous Baxter T-Q equations. The two families satisfy an inhomogeneous quantum Wronskian equation.

Key words: integrable spin chain; algebraic Bethe ansatz; Baxter T-Q equation; quantum Wronskian equation.

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