Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models

Abstract

In this work, we construct an alternative formulation to the traditional Algebraic Bethe ansatz for quantum integrable models derived from a generalised rational Gaudin algebra realised 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.

26 pages, 0 figure, published version

References in corpus (5)

• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Solving the Richardson equations close to the critical points
• On the determinant representations of Gaudin models' scalar products and form factors
• Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model

Cited by in corpus (3)

• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• A variational method for integrability-breaking Richardson-Gaudin models
• Exact solution for the inhomogeneous Dicke model in the canonical ensemble: thermodynamical limit and finite-size corrections