Electrostatic analogy for integrable pairing force Hamiltonians

TL;DR

This paper extends the electrostatic analogy used in the exactly solvable reduced BCS model to a broader class of integrable pairing Hamiltonians, enabling exact thermodynamic analysis and validation through numerical solutions.

Contribution

It introduces an electrostatic analogy for a wider class of integrable pairing Hamiltonians, facilitating their thermodynamic limit analysis.

Findings

Derived the electrostatic analogy for new integrable models.

Obtained the exact thermodynamic limit for these models.

Validated analytical results with numerical solutions.

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.