Numerical algorithm for the standard pairing problem based on the Heine–Stieltjes correspondence and the polynomial approach

Published: 01-01-2014| Version 1 | DOI: 10.17632/xjks9p7f5v.1
Xin Guan,
Kristina D. Launey,
Mingxia Xie,
Lina Bao,
Feng Pan,
Jerry P. Draayer


Abstract We present a detailed study of the computational complexity of a numerical algorithm based on the Heine–Stieltjes correspondence following the new approach we proposed recently for solving the Bethe ansatz (Gaudin–Richardson) equations of the standard pairing problem. For k pairs of valence nucleons in n non-degenerate single-particle energy levels, the approach utilizes that solutions of the Bethe ansatz equations can be obtained from two matrices of dimensions ( k + 1 ) × ( k + 1 ) and ( n ... Title of program: exactPairingHS Catalogue Id: AETD_v1_0 Nature of problem The program calculates exact pairing energies based on the Heine-Stieltjes polynomial approach. Existing conventional exact-pairing approaches require solving systems of highly nonlinear equations, which are difficult and often impossible to solve beyond the simplest of the quantum-mechanical many-particle systems. In this study, the Heine-Stieltjes polynomial approach is employed to provide solutions for more than one or two pairs of particles residing in many energy levels. Versions of this program held in the CPC repository in Mendeley Data AETD_v1_0; exactPairingHS; 10.1016/j.cpc.2014.05.023 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)