Richardson-Gaudin models and broken integrability

Abstract

This thesis presents an introduction to the class of Richardson-Gaudin integrable models, with special focus on the Bethe ansatz wave function, and investigates ways of applying the properties of Richardson-Gaudin models both in and out of integrability. A framework is outlined for the numerical and theoretical treatment of these systems, exposing a duality allowing the Bethe equations to be solved numerically. This is extended to the calculation of inner products and correlation functions. Using this framework, the influence of particle exchange on the Bethe ansatz is discussed, after which it is shown how the Bethe ansatz is able to accurately model wave functions of non-integrable models in two different settings. First, a variational approach is outlined for stationary models where integrability-breaking perturbations are explicitly introduced. Second, an alternative way of breaking integrability is through the introduction of dynamics and periodic driving, where it is shown how integrability can be used to model the resulting Floquet many-body resonances. Throughout this work, it is shown how the clear-cut structure and relatively large freedom in Richardson-Gaudin models makes them ideal for an investigation of the general principles of integrability, as well as being a perfect testing ground for the development of new quantum many-body techniques beyond integrability.

PhD Thesis (174 pages), Ghent University, 2018, ISBN 978-9-4619761-4-7

References in corpus (4)

• Equilibrium states of generic quantum systems subject to periodic driving
• Floquet control of quantum dissipation in spin chains
• Avoided level crossing spectroscopy with dressed matter waves
• Spin polarization through Floquet resonances in a driven central spin model

Cited by in corpus (7)

• Entanglement and collective flavor oscillations in a dense neutrino gas
• Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem
• Reduced Density Matrices / Static Correlation Functions of Richardson-Gaudin States Without Rapidities
• Persistent dark states in anisotropic central spin models
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• Integrable active atom interferometry
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models