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

Details Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence

2011-03-02

arxiv.org/abs/1103.0472v3

Phys. Rev. B 83, 235124 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 3 figures, published version

Scientific paper

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 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.

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