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Dynamics of Probed, Pulsed, Quenched and Driven Integrable Quantum Systems

Periodic Reporting for period 3 - DYNAMINT (Dynamics of Probed, Pulsed, Quenched and Driven Integrable Quantum Systems)

Reporting period: 2020-09-01 to 2022-02-28

This project's main thrust is to develop a new theoretical toolbox for understanding the dynamics of strongly-interacting many-body quantum sytems "stirred" or "shaken" out of equilibrium.

Quantum matter is routinely pushed out of its equilibrium comfort zone by experiments on atomic systems, condensed matter and nanophysics devices. The problem is that theory is often unable to follow: the traditional toolbox fails; in fact, some experiments even clearly highlight the need to revise basic fundamental quantum statistical mechanics notions such as ergodicity, relaxation and thermalization in order to explain their behaviour.

This project is focused on a set of systems which have the potential to reveal secrets of out-of-equilibrium quantum matter: exactly-solvable models of quantum spin chains, interacting gases confined to one spatial dimension, and quantum dots.

The project is implementing a broad research agenda using tools ranging from mathematically formal thought experiments all the way to phenomenologically applied practical calculations. The types of protocols studied include probes creating high-energy excitations, pulses inducing changes beyond linear response, quenches causing sudden global reorganizations, all the way to drivings completely metamorphozing the physical states.

This project's overall objective is to use these solvable settings to put theory on the right road towards understanding and controlling driven quantum matter.
During the first phase of the implementation of this project, we have addressed some of the main goals of the proposal. These are explained in more details in the Scientific Report.

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. In a more recent development, the Generalized Hydrodynamics method has been extended to the case of space- and time-dependent interactions.

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 started providing 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.
A number of methods developed to achieve the points above have gone beyond the state of the art.

The use of integrable wavefunctions as a basis for variational optimizations has the potential to also be useful for other models.

The new space- and time-dependent interaction version of Generalized Hydrodynamics can be used to suggest and model experiments in cold atoms.

On Floquet systems, the games we have played with Floquet resonances have the potential to generate new productive ideas on how to dynamically achieve target state preparation (a new form of optimal control).
Finally, the apparatus of numerical renormalization using Bethe states mixes the most advanced integrability machinery available with the long-established power of numerical renormalization, and is yielding powerful insights into how renormalization can be implemented in a much more powerful and efficient manner than current versions.