Dynamical correlation functions of the mesoscopic pairing model

Abstract

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.

References in corpus (6)

• Dynamical density-density correlations in the one-dimensional Bose gas
• Exact dynamics in the inhomogeneous central-spin model
• Quantum quenches from integrability: the fermionic pairing model
• Thermodynamics of pairing in mesoscopic systems
• Solving the Richardson equations close to the critical points
• Density correlations in ultracold Fermi systems within the exact Richardson solution

Cited by in corpus (2)

• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• BEC-BCS crossover in a p+ip-wave pairing Hamiltonian coupled to bosonic molecular pairs