Algebraic Bethe ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models
In this work, we construct an alternative formulation to the traditional algebraic Bethe ansätze for quantum integrable models derived from a generalized rational Gaudin algebra realized in terms of a collection of spins 1/2 coupled to a single bosonic mode. The ensemble of resulting models which we call Dicke-Jaynes-Cummings-Gaudin models are particularly relevant for the description of light-matter interaction in the context of quantum optics. Having two distinct ways to write any eigenstate of these models we then combine them in order to write overlaps and form factors of local operators in terms of partition functions with domain wall boundary conditions. We also demonstrate that they can all be written in terms of determinants of matrices whose entries only depend on the eigenvalues of the conserved charges. Since these eigenvalues obey a much simpler set of quadratic Bethe equations, the resulting expressions could then offer important simplifications for the numerical treatment of these models.
Journal of Physics A Mathematical General
- Pub Date:
- October 2014
- Mathematical Physics;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- 26 pages, 0 figure, published version