Gaudin models solver based on the Bethe ansatz/ordinary differential   equations correspondence
  We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the coupling strength no longer appear explicitly. The problem is thus reduced to a set of quadratic algebraic equations. The required inverse transformation can then be realized using only linear operations and a standard polynomial root finding algorithm. The method is applied to Richardson's fermionic pairing model, the central spin model and generalized Dicke model. 
Alexandre Faribault, Omar El Araby, Christoph Str\"ater, Vladimir   Gritsev
cond-mat.mes-hall cond-mat.supr-con quant-ph