scholarly journals Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models

2021 ◽  
pp. 115424
Author(s):  
T. Skrypnyk ◽  
N. Manojlović
Keyword(s):  
Bethe Ansatz ◽  
Algebraic Bethe Ansatz

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.

On a long range variant of the discrete NLS equation and algebraic Bethe ansatz

1996 ◽  
Vol 53 (2) ◽  
pp. 129-132 ◽  
Author(s):  
A Ghose Choudhury ◽  
A Roy Chowdhury
Keyword(s):  
Bethe Ansatz ◽  
Long Range ◽  
Nls Equation ◽  
Algebraic Bethe Ansatz

scholarly journals Algebraic Bethe ansatz for the eight-vertex model with general open boundary conditions

1996 ◽  
Vol 478 (3) ◽  
pp. 723-757 ◽  
Author(s):  
Heng Fan ◽  
Bo-yu Hou ◽  
Kang-jie Shi ◽  
Zhong-xia Yang
Keyword(s):  
Boundary Conditions ◽  
Bethe Ansatz ◽  
Open Boundary ◽  
Vertex Model ◽  
Open Boundary Conditions ◽  
Algebraic Bethe Ansatz
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