Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Articles dans des revues à comité de lecture

Gaudin models solver based on the correspondence between Bethe ansatz and ordinary differential equations
Faribault A., El Araby O., Straeter C., Gritsev V.
PHYSICAL REVIEW B 83 (2011) 235124
DOI : 10.1103/PhysRevB.83.235124

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a different 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 the generalized Dicke model.



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