Order parameter, correlation functions and fidelity susceptibility for the BCS model in the thermodynamic limit

Abstract

The exact ground state of the reduced BCS Hamiltonian is investigated numerically for large system sizes and compared with the BCS ansatz. A "canonical'' order parameter is found to be equal to the largest eigenvalue of Yang's reduced density matrix in the thermodynamic limit. Moreover, the limiting values of the exact analysis agree with those obtained for the BCS ground state. Exact results for the ground state energy, level occupations and a pseudospin-pseudospin correlation function are also found to converge to the BCS values already for relatively small system sizes. However, discrepancies persist for a pair-pair correlation function, for inter-level correlations of occupancies and for the fidelity susceptibility, even for large system sizes where these quantities have visibly converged to well-defined limits. Our results indicate that there exist non-perturbative corrections to the BCS predictions in the thermodynamic limit.

11 pages, 14 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models
• On the determinant representations of Gaudin models' scalar products and form factors
• Ground-state fidelity in the BCS-BEC crossover
• BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function

Cited by in corpus (5)

• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• Integrability and dark states in an anisotropic central spin model
• Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models
• A variational method for integrability-breaking Richardson-Gaudin models
• Applicability of Bardeen-Cooper-Schrieffer theory to small-sized superconductors: role of Cooper-pair binding energy