Ground-state energy of a Richardson-Gaudin integrable BCS model
arXiv:1912.05692 · doi:10.21468/SciPostPhysCore.2.1.001
Abstract
We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.
arXiv commentSubmission to SciPost, 17 pages, no figures. This version is a minor modification, in response to referee comments
References in corpus (21)
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Exactly solvable Richardson-Gaudin models for many-body quantum systems
- Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
- Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
- Quantum phase diagram of the integrable p_x+ip_y fermionic superfluid
- Large N limit of the exactly solvable BCS model: analytics versus numerics
- Exactly solvable pairing model for superconductors with a p+ip-wave symmetry
- An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
- On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
- Exact solution of the p+ip pairing Hamiltonian and a hierarchy of integrable models
- Exact solution of the pairing Hamiltonian by deforming the pairing algebra
- On the determinant representations of Gaudin models' scalar products and form factors
- Read-Green resonances in a topological superconductor coupled to a bath
- Electrostatic analogy for integrable pairing force Hamiltonians
- Solution of the classical Yang--Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunneling model
- Inner products in integrable Richardson-Gaudin models
- An integrable case of the p+ip pairing Hamiltonian interacting with its environment
- Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field
- Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
- Ground-state energies of the open and closed -pairing models from the Bethe Ansatz
- Read-Green points and level crossings in XXZ central spin models and topological superconductors