Periodic Reporting for period 2 - NEQuM (Non-Ergodic Quantum Matter: Universality, Dynamics and Control)
Periodo di rendicontazione: 2021-08-01 al 2023-01-31
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.
During the first funding period we focused mostly on exploring dynamics and eigenstates of non-ergodic systems. In particular, we addressed the question of existence of mobility edges in the many-body localized systems. In this work we studied both eigenstates and dynamics, and pushed the matrix product states time evolution methods beyond the state of the art. In addition, a significant progress was achieved on theoretical description of quantum many-body scars. In particular, theoretical work and experimental collaboration with Lukin’s group (Harvard univ.) confirmed the existence of quantum many-body scars in two dimensional systems of Rydberg atoms. 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.
The results obtained during this reporting period are beyond the state of the art. In particular, 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. Moreover, we developed new analytical and numerical techniques to address the properties of quantum many-body scars, based on tensor networks and algebraic methods.
Towards the end of the 5 year period we expect to have an advanced method toolbox for accessing eigenstates, dynamics, and controlling non-ergodic systems.
Towards the end of the 5 year period we expect to have an advanced method toolbox for accessing eigenstates, dynamics, and controlling non-ergodic systems.