Séminaire de Physique Théorique«Bethe ansatz free» solution of integrable spin-1/2 Richardson-Gaudin models
Alexandre Faribault (Université de Lorraine)
Monday 10 December 2018 13:00 - Tours - Salle 1180 (Bât E2)
In this work, we first show how simple operator-level relations between conserved charges of the spin-1/2 Richardson-Gaudin models are sufficient to access their eigenvalue spectrum. One can then do so without having to define a Bethe ansatz solution to the problem, therefore, avoiding any possible complications linked to the absence of U(1) symmetry in fully anisotropic XYZ models. The resulting equations give the eigenvalues of the models as the set of solutions to a system of quadratic equations, which provides a much simpler route, numerically speaking, than the usual equations linking the Bethe roots. We then demonstrate that this eigenvalue-based approach also allows one to construct the eigenstates of these models. The proposed representation of the eigenstates is built explicitly only in terms of the conserved charges themselves and the set of eigenvalues and therefore, once again, completely bypasses any Bethe Ansatz approach. In doing so, the whole class of quantum integrable models discussed here, even the models without U(1) symmetry, become amenable to the same simple "Bethe Ansatz free” solution.