2015/06/11 by Pieter W. Claeys, Stijn De Baerdemacker, Mario Van Raemdonck +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Integrable system #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pairing #Physics #Quadratic equation #Quantum mechanics #Scalar (mathematics) #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/42/425201
published as J. Phys. A: Math. Theor. 48 425201 (2015)
arxiv created 2015/06/11 · openalex publication_date 2015/09/22 · arxiv updated 2015/11/16 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Starting from integrable su (2) (quasi-)spin Richardson–Gaudin (RG) XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke–Jaynes–Cummings–Gaudin models and the two-channel ( p + i p )-wave pairing Hamiltonian. The pseudo-deformation of the underlying su (2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke–Jaynes–Cummings–Gaudin models with the general results for RG XXZ models.