Skip to main content

Thermalization of out-of-equilibrium quantum matter

Periodic Reporting for period 1 - ThermOutOfEq (Thermalization of out-of-equilibrium quantum matter)

Reporting period: 2018-05-01 to 2020-04-30

"The topic of this project is the theoretical understanding of quantum systems involving a large number of interacting degrees of freedom. In general, systems of this kind exhibit chaotic dynamics which brings them to thermal equilibrium, where the state is completely described by the temperature. Here, we focus to the situation where the system is perturbed by the presence of an external drive. In particular, settings where the drive strength can be considered weak are important because they lead to a separation of time scale: because of its intrinsic chaotic dynamics, the system is capable of thermalising and it reaches an equilibrium state; however because of the weak drive, the equilibrium state slowly changes in time. This ""quasi-equilibrium"" regime allows for an effective and controlled treatment because only the dynamics of a few parameters (generalized temperatures conjugated to the conserved quantities) has to be taken into account.
Novel phases of matter can emerge at large times by engineering experimental setups where the competition between the tendency toward equilibrium of the system itself and the drive result in interesting physical phenomena (long-range order, cooling effects, etc). An important example considered in detail is dynamic nuclear polarization (DNP), with promising application for medical imaging. DNP is a protocol used in nuclear magnetic resonance (NMR) to increase the nuclear polarization in a compound doped doped with unpaired electron spins. The compound is driven by turning on a microwave irradiation: then, the interacting spin system of electrons and nuclei reorganizes itself in an out-of-equilibrium steady state characterized by an enhanced nuclear polarization, due to an extremely low effective temperature. This setup emerges exactly in the regime of weak dissipation/drive at the centre of this programme.

As a second important aspect, we focus on those effects which can prevent the emergence of chaotic dynamics. This phenomenon is named ""many-body localization"" (MBL) as it signals the tendency of the system to remain stuck close to its initial configuration. It is possible in a quantum setup in the presence of strong disorder and sufficiently weak interactions. MBL was theoretically conjectured in the last ten years and has received experimental confirmation. In this case, we consider the effect of a weak drive on a system which becomes less and less chaotic because of the presence of many-body localization. The combination of MBL and a drive is at the origin of the intriguing mechanism of time crystals, but further technological applications (quantum memory, quantum computation, etc.) can be imagined in the near future.

Aim of this programme is therefore to reach a full theoretical understanding of disordered weakly driven/dissipative systems, providing clear experimental signatures of MBL and increasing the control in the ergodic phase for applications."
"The main difficulty in the theoretical study of many-body quantum systems is the exponental complexity of their space of configurations. To overcome this difficulty in the framework of this project, we followed two strategies: 1) the use of a ""important sampling strategy"", where only a small fractions of relevant configurations are visited thanks to the combination of a renormalization group and Montecarlo algorithms; 2) the use of tensor network and matrix product states (MPS) which are extremely efficient in those situations where entanglement production is suppressed. Both approaches have advantages and weaknesses, but their combination allows us to develop a physical intuition. For instance, MPS helped us in the analysis of a Heisenberg XXZ spin chain, driven by the presence of a time dependent magnetic flux: this unveiled a novel kind of phase transition between reversible and irreversible dynamics where entanglement production suddenly starts [A. Bastianello, ADL, PRL, 122 , 240606].

On a more fundamental side, we studied generic features of chaotic systems driven by a periodic drive (Floquet). By using Floquet random circuit, we unveiled universal features of quantum chaos which appear in the statistic of matrix elements. It had been observed for some time that for a quantum chaotic system, matrix elements of local operators have a distribution that resembles the one of a random matrix. Our analysis confirmed this conjecture but also unveiled that subleading correlations appear between higher order correlators (e.g. products of four matrix elements): these correlations are universal as they are the direct consequence of the butterfly effect in a system with local interactions [A. Chan, ADL, J. T. Chalker, PRL 122, 220601 (2019)]."
The proposal has been terminated earlier because the fellow has been appointed as a permanent CNRS researcher in France: this already testifies that this project was crucial to develop his network of collaborations and establish him as a leader in the field.

Additionally, the results obtained so far within this fellowship will have an impact in several research fields connected with the out-of-equilibrium dynamics of driven quantum systems. For instance the numerical algorithm based on renormalization ond montecarlo will be of use for the dynamics of driven systems in the presence of strong disorder. In the particular case of dynamic nuclear polarization, this numerical procedure has the potential to improve the efficiency of the protocol by further optimizing the experimental parameters. At the same time, it will provide novel methods to investigate the available mechanisms of ergodicity breaking.

Additionally, research developed in this first part has highlighted how integrability can be used to preserve the reversibility of quantum dynamics.

The study of periodically driven systems via the use of Floquet random circuit has provided a novel framework to the study of quantum chaos: it will have a longstanding impact, both in deepening our fundamental understanding about the mechanisms behind thermalization and quantum dynamics, as well as in technological applications and experiments. Additionally, within this project, the study of entanglement dynamics in the presence of continuous monitoring was started. This paved the way to the study of a novel kind of entanglement phase transition between area law and volume law, induced by the measurement rate.

Controlling the development of dissipation and decoherence, the production of entanglement in generic systems both induced by the intrinsic chaotic dynamics and by the external action of a quantum feedback will have important effects on future technological applications, related to the development of quantum memories, quantum computation and metrology.
Entanglement entropy as a function of the time-dependent magnetic flux [PRL, 122 , 240606 (2019)].