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.

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Cited by in corpus (11)

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• Density Matrices of Seniority-Zero Geminal Wavefunctions
• Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
• Reduced Density Matrices / Static Correlation Functions of Richardson-Gaudin States Without Rapidities
• Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime
• BEC-BCS crossover in a p+ip-wave pairing Hamiltonian coupled to bosonic molecular pairs
• Read-Green points and level crossings in XXZ central spin models and $p_x+i{p}_y$ topological superconductors
• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
• Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field