The paper identifies the Richardson Yang-Yang function with a Gaiotto-Witten irregular Virasoro block and provides a numerical solver for the Bethe equations of Richardson-Gaudin models.
Integrability of the pairing hamiltonian
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abstract
We show that a many-body Hamiltonian that corresponds to a system of fermions interacting through a pairing force is an integrable problem, i.e. it has as many constants of the motion as degrees of freedom. At the classical level this implies that the Time-dependent Hartree-Fock- Bogoliubov dynamics is integrable and at the quantum level that there are conserved operators of two-body character which reduce to the number operators when the pairing strength vanishes. We display these operators explicitly and study in detail the three-level example.
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2D CFT and efficient Bethe ansatz for exactly solvable Richardson-Gaudin models
The paper identifies the Richardson Yang-Yang function with a Gaiotto-Witten irregular Virasoro block and provides a numerical solver for the Bethe equations of Richardson-Gaudin models.