Omar El Araby, Dionys Baeriswyl
The exact ground state of the reduced BCS Hamiltonian with a non-degenerate single-particle spectrum is investigated numerically for large system sizes (up to 4000 levels) and compared with the BCS ansatz. While generic quantities such as the total energy or the superconducting order parameter are found to converge to the BCS values already for relatively small system sizes, other quantities, in particular the ground state fidelity susceptibility and a pair correlation function involving HOMO and LUMO levels, do not agree with BCS theory, even for large system sizes where they have visibly converged to well-defined limits. The discrepancies are particularly large in the intermediate coupling range. We conclude that the BCS wave function does not represent the exact ground state of the reduced BCS Hamiltonian.
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http://arxiv.org/abs/1304.0628
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