Integrability of an extended d+id-wave pairing Hamiltonian

Abstract

We introduce an integrable Hamiltonian which is an extended d+id-wave pairing model. The integrability is deduced from a duality relation with the Richardson-Gaudin (s-wave) pairing model, and associated to this there exists an exact Bethe ansatz solution. We study this system using the continuum limit approach and solve the corresponding singular integral equation obtained from the Bethe ansatz solution. We also conduct a mean-field analysis and show that results from these two approaches coincide for the ground state in the continuum limit. We identify instances of the integrable system where the excitation spectrum is gapless, and discuss connections to non-integrable models with d+id-wave pairing interactions through the mean-field analysis.

7 pages, 1 figure

References in corpus (9)

• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Quantum quenches from integrability: the fermionic pairing model
• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Solving the Richardson equations close to the critical points
• Exact expectation values within Richardson's approach for the pairing Hamiltonian in a macroscopic system
• "Probabilistic" approach to Richardson equations
• Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime
• Boundary Wess-Zumino-Novikov-Witten Model from the Pairing Hamiltonian
• A variational approach for the Quantum Inverse Scattering Method

Cited by in corpus (8)

• Transient Dynamics of d-wave Superconductors after a Sudden Excitation
• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• Consequences of integrability breaking in quench dynamics of pairing Hamiltonians
• Integrability and duality in spin chains
• Ground-state energies of the open and closed $p+ip$-pairing models from the Bethe Ansatz
• Ground-state Bethe root densities and quantum phase transitions
• Non-adiabatic dynamics in d+id-wave fermionic superfluids
• Solvable 2D superconductors with l-wave pairing