Non-Ergodic Quantum Matter: Universality, Dynamics and Control

Project Information

NEQuM

Grant agreement ID: 850899

DOI

10.3030/850899

Project closed

EC signature date 18 September 2019

Start date 1 February 2020

End date 31 January 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 498 420,00

EU contribution

€ 1 498 420,00

Coordinated by

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Austria

Periodic Reporting for period 4 - NEQuM (Non-Ergodic Quantum Matter: Universality, Dynamics and Control)

Reporting period: 2024-08-01 to 2025-01-31

Summary of the context and overall objectives of the project

The main goal of this project is to develop theory of non-equilibrium quantum systems that avoid thermal equilibrium. This theory aims to scope such properties of these systems as their eigenstates, dynamics and ways to control them. This problem touches the fundamental question of how/when statistical mechanics fails to emerge in isolated quantum systems that consist of many interacting particles. On the one hand, the expectation is that from understanding examples of breakdown of thermalization we also learn new insights into thermalization – a fundamental insights into laws of nature. On the other hand, the non-ergodic quantum system may have potential uses in storing and manipulating quantum information thus being helpful in the ongoing effort towards scalable quantum computations. The theory of the non-ergodic systems developed in this grant may help in both directions.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

During the duration of the project we studied dynamics and eigenstates of non-ergodic systems such as many-body localized systems and quantum many-body scars, also devised novel ways for quantum control. Main result include:
1. existence of mobility edges in the many-body localized systems.
2. study of many-body localized eigenstates and dynamics, and pushing the matrix product states time evolution methods beyond the state of the art
3. theoretical description of quantum many-body scars and experimental collaboration with Lukin’s group (Harvard univ.) confirmed the existence of quantum many-body scars in two dimensional systems of Rydberg atoms.
4. using results for scars, we constructed theory explaining experiments and devised ways of controlling dynamics of quantum scars via the periodic driving – an important milestone in the third direction of controlling non-ergodic systems
5. we created new method for control of many-body quantum systems along a given trajectory in the state space
These results, and many others, were disseminated at a more than 30 conferences and workshops, as well as in press releases and social media.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The results obtained during this project are beyond the state of the art. In particular, we obtained
1. numerical simulations of the dynamics of many-body localized systems used parallel algorithm and achieved very large bond dimensions needed to capture the large entanglement present in the system
2. new analytical and numerical techniques to address the properties of quantum many-body scars, based on tensor networks and algebraic methods
3. new tensor networks based approaches for quantum control and obtaining Floquet eigenstates with tensor networks
Therefore the project advanced methods for accessing eigenstates, dynamics, and controlling non-ergodic systems.

Improving quantum scars by periodic driving