Dynamical correlation functions of the mesoscopic pairing model

Details Dynamical correlation functions of the mesoscopic pairing model Dynamical correlation functions of the mesoscopic pairing model

2010-03-02

arxiv.org/abs/1003.0582v1

Phys. Rev. B 81, 174507 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevB.81.174507

We study the dynamical correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact expressions for the form factors of the most important observables. By summing these form factors over a relevant set of states, we obtain very precise estimates of the correlation functions, as confirmed by global sum-rules (saturation above 99% in all cases considered). Unlike the case of many other Bethe Ansatz solvable theories, simple two-particle states are sufficient to achieve such saturations, even in the thermodynamic limit. We provide explicit results at half-filling, and discuss their finite-size scaling behavior.

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