scholarly journals Algebraic Bethe Ansatz for the Trigonometric sℓ(2) Gaudin Model with Triangular Boundary

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 352
Author(s):  
Nenad Manojlović ◽  
Igor Salom

In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.

Author(s):  
Nikolai Kitanine ◽  
◽  
Giridhar Kulkarni ◽  
◽  
◽  
...  

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.


2011 ◽  
Vol 52 (10) ◽  
pp. 103501
Author(s):  
N. Cirilo António ◽  
N. Manojlović ◽  
A. Stolin

2015 ◽  
Vol 893 ◽  
pp. 305-331 ◽  
Author(s):  
N. Cirilo António ◽  
N. Manojlović ◽  
E. Ragoucy ◽  
I. Salom

1994 ◽  
Vol 33 (3) ◽  
pp. 679-685
Author(s):  
Nibedita Bhattacharya ◽  
A. Roy Chowdhury

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