Electron-hole symmetry and solutions of Richardson pairing model

Abstract

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.

9 pages, 1 figure; accepted for publication in Eur. Phys. J. B

References in corpus (4)

• Isovector neutron-proton pairing with particle number projected BCS
• Exact expectation values within Richardson's approach for the pairing Hamiltonian in a macroscopic system
• "Probabilistic" approach to Richardson equations
• Density correlations in ultracold Fermi systems within the exact Richardson solution

Cited by in corpus (5)

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• Applicability of Bardeen-Cooper-Schrieffer theory to small-sized superconductors: role of Cooper-pair binding energy
• Particle-hole duality, integrability, and Russian doll BCS model