A variational method for integrability-breaking Richardson-Gaudin models
arXiv:1707.06793 · doi:10.1103/PhysRevB.96.155149
Abstract
We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. The method is shown to return exact results for integrable models and improve substantially on perturbation theory for models close to integrability. For large integrability-breaking interactions, it is shown how (avoided) level crossings necessitate the use of excited states of integrable Hamiltonians in order to accurately describe the ground states of general non-integrable models.
References in corpus (16)
- Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
- The ODE/IM Correspondence
- Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
- Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
- Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
- An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
- Richardson-Gaudin integrability in the contraction limit of the quasispin
- Characterization of resonances using finite size effects
- Solving the Richardson equations close to the critical points
- On the determinant representations of Gaudin models' scalar products and form factors
- Inner products in integrable Richardson-Gaudin models
- Algebraic Bethe Ansätze and eigenvalue-based determinants for Dicke-Jaynes-Cummings-Gaudin quantum integrable models
- Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
- Different types of integrability and their relation to decoherence in central spin models
- Competing interactions in semiconductor quantum dots
- BEC-BCS crossover in a p+ip-wave pairing Hamiltonian coupled to bosonic molecular pairs