title: The Andreev states of a superconducting quantum dot: mean field versus exact numerical results.
abstract: We analyze the spectral density of a single level quantum dot coupled  to superconducting leads focusing on the Andreev states appearing within the superconducting gap. We use two complementary approaches: the numerical renormalization group and the Hartree-Fock approximation. Our results show the existence of up to four bound states within the gap when the ground state is a spin doublet (π phase). Furthermore the results demonstrate the reliability of the mean field description within this phase. This is understood from a complete correspondence that can be established between the exact and the mean field quasiparticle excitation spectrum within the gap.
authors.affiliation: Departamento de Física Teórica de la Materia Condensada and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Martín-Rodero
authors.forename: A Levy
authors.initials: AL
authors.lastname: Yeyati