Faculté des sciences

Gaudin models solver based on the correspondence between Bethe ansatz and ordinary differential equations

Faribault, Alexandre ; Araby, Omar El ; Sträter, Christoph ; Gritsev, Vladimir

In: Physical Review B Condensed Matter and Materials Physics, 2011, vol. 83, no. 23, p. 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... Plus

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    Summary
    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.