During the implementation of this project, we have addressed a large number of the main goals of the original proposal.
Integrability breaking has been studied in the context of central spin/Richardson models. Using Bethe Ansatz-based variational wavefunctions, the ground states of systems close to integrability have been constructed. By including excited states in the description, the idea was also shown to be extensible to more general nonintegrable models.
The dynamics of atomic gases quenched from an initial spatially inhomogeneous state has been investigated using Generalized Hydrodynamics, for which we have provided an effective implementation in terms of the "flea gas" algorithm. In particular, the setup of the famous Quantum Newton's Cradle has been simulated including important experimental details such as the trapping potential. The Generalized Hydrodynamics method has been extended to the case of space- and time-dependent interactions. This has been used to study experimentally-motivated bound-state formation in interacting cold atomic systems.
On the proposal's pillar concerning driven systems and Floquet dynamics, driven magnetic systems such as the central spin and Heisenberg models have been shown to display interesting Floquet resonances allowing to realize targeted state preparation with judiciously-chosen time-dependent protocols.
Transport problems in out-of-equilibrium fermionic gases quenched from asymmetrically-filled initial states have been investigated using analytical methods, providing insights into time-dependent currents, shot noise and entanglement.
One of the other pillars of the proposal, numerical renormalization using Bethe states as basis, has provided extensive results: for Lieb-Liniger gases perturbed by local density operator moments, we have obtained detailed perturbed wavefunction representations as well as detailed post-quench time evolution data.
Building up on the research line adoped in the proposal, a new class of Hilbert space scanning algorithms has been developed which substantially accelerates computations of dynamical properties of integrable models for finite-entropy states.
Integrability-based results have also been used to describe inelastic neutron scattering experiments, focusing on traditionally difficult to access small small/time separations.
