scholarly journals Algebraic Bethe ansatz solutions for thesl(2|1)(2)andosp(2|1) models with boundary terms

2005 ◽  
Vol 38 (11) ◽  
pp. 2359-2373 ◽  
Author(s):  
V Kurak ◽  
A Lima-Santos
Keyword(s):  
Bethe Ansatz ◽  
Algebraic Bethe Ansatz ◽  
Boundary Terms

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
Keyword(s):  
Bethe Ansatz ◽  
Generating Function ◽  
Periodic Case ◽  
Gaudin Model ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Boundary Terms ◽  
Reflection Matrix ◽  
Bethe Equations

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.

scholarly journals Introduction to the nested algebraic Bethe ansatz

2020 ◽  
Author(s):  
Nikita Slavnov
Keyword(s):  
Bethe Ansatz ◽  
Trace Formula ◽  
Integrable Models ◽  
Explicit Formulas ◽  
Algebraic Bethe Ansatz

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a \mathfrak{gl}_3𝔤𝔩3-invariant RR-matrix as the basic example, however, we also describe possible generalizations. We give recursions and explicit formulas for the Bethe vectors. We also give a representation for the Bethe vectors in the form of a trace formula.

Quantum Tavis–Cummings Model

2019 ◽  
pp. 474-488
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Strong Interaction ◽  
Building Blocks ◽  
Vertex Model ◽  
Algebraic Bethe Ansatz ◽  
Quantum Matter ◽  
Ansatz Approach

This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum matter. In the case of the quantum Tavis–Cum- mings model there is no underlying vertex model to suggest the constituent building blocks of the algebraic Bethe ansatz approach, e.g.like the L-matrix or ultimately the transfer matrix. The algebraic Bethe ansatz is then first applied to the Tavis–Cummings Hamiltonian with an added Stark term using a conjecture for the transfer matrix. The original Tavis–Cummings model and its algebraic Bethe ansatz are obtained in the limit of vanishing Stark term, which requires considerable care.

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