Periodic Reporting for period 4 - DYNAMINT (Dynamics of Probed, Pulsed, Quenched and Driven Integrable Quantum Systems)
Reporting period: 2022-03-01 to 2023-08-31
This project's main thrust was 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 was 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 implemented 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 included 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.
The project delivered a number of achievements including theoretical advances on the use of integrability in renormalization, hydrodynamics, driven systems and in the description of experiments on quantum magnets.
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 was 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 implemented 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 included 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.
The project delivered a number of achievements including theoretical advances on the use of integrability in renormalization, hydrodynamics, driven systems and in the description of experiments on quantum magnets.
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.
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.
A number of methods developed to achieve the points above have gone beyond the state of the art:
- the use of Bethe wavefunctions as variational wavefunctions
- numerical renormalization techniques based on and leveraging the power of quantum integrability
- a "flea gas" algorithm for rapid computations within generalized hydrodynamics
- generalized hydrodynamics methods for situations with general space- and time-dependent potentials
- the development of state preparation methods based on Floquet resonances through a generalization of the logic of Landau-Zener transitions
- Hilbert space scanning algorithms to efficiently sum intermediate-state contributions in calculations of dynamical properties of integrable models
- fermionic determinant-based resummation methods to capture effects of strong correlations in quantum gases
Although the project has ended, there are still a number of results to be expected, mostely in the form of
extensive data on dynamics of atomic gases and spin chains.
- the use of Bethe wavefunctions as variational wavefunctions
- numerical renormalization techniques based on and leveraging the power of quantum integrability
- a "flea gas" algorithm for rapid computations within generalized hydrodynamics
- generalized hydrodynamics methods for situations with general space- and time-dependent potentials
- the development of state preparation methods based on Floquet resonances through a generalization of the logic of Landau-Zener transitions
- Hilbert space scanning algorithms to efficiently sum intermediate-state contributions in calculations of dynamical properties of integrable models
- fermionic determinant-based resummation methods to capture effects of strong correlations in quantum gases
Although the project has ended, there are still a number of results to be expected, mostely in the form of
extensive data on dynamics of atomic gases and spin chains.
