Electrostatic analogy for integrable pairing force Hamiltonians

Abstract

For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.

14 pages, 6 figures, revtex4. Minor changes

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• Exact solution of the p+ip pairing Hamiltonian and a hierarchy of integrable models
• Richardson-Gaudin integrability in the contraction limit of the quasispin
• Exact quantum dynamics of XXZ central spin problems
• What are the elementary excitations of the BCS model in the canonical ensemble?
• Quasi-classical descendants of disordered vertex models with boundaries
• The extended Heine-Stieltjes polynomials associated with a special LMG model
• Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
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• Exact solution of the p+ip Hamiltonian revisited: duality relations in the hole-pair picture
• Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime
• The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity
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• Exact solution for the inhomogeneous Dicke model in the canonical ensemble: thermodynamical limit and finite-size corrections
• Density correlations in ultracold Fermi systems within the exact Richardson solution
• Ground-state energy of a Richardson-Gaudin integrable BCS model
• Exactly solvable discrete BCS - type Hamiltonians and the Six-Vertex model
• Particle-hole duality, integrability, and Russian doll BCS model
• On the exactly solvable pairing models for bosons
• Exact ground-state correlation functions of an atomic-molecular boson conversion model
• Mesoscopic BCS pairing in the repulsive 1d-Hubbard model
• Fermi Surface Volume of Interacting Systems