In the last decade our fundamental understanding of non-equilibrium quantum matter has undergone a paradigmatic change. The theoretical prediction of time crystals and non-ergodic states in disordered, isolated systems has led to exciting developments in quantum many-body physics, including the experimental detection of these novel phases in solid state and engineered quantum systems. Although strongly interacting, these states preserve their quantum characteristics at large distances and long times, provided they are well isolated. One of the conceptual difficulties in connecting theory to experiment is the role of environment. Therein lies a fundamental challenge of describing these novel non-equilibrium states in the presence of dissipation.
This project developed the theoretical principles governing the effects of dissipation on time-crystallinity and ergodicity-breaking in periodically driven and disordered systems. By studying the relaxation properties of such systems in the presence of dissipation, the dynamical regimes of non-ergodic and time-crystalline systems were classified. Furthermore, the dependence of relaxation time scales on the spectral properties and degree of Markovianity of the environment were studied. This could provide useful insights into the distinction between non-ergodic quantum phases and classical glasses, with potential applications for future quantum devices.
The project investigated the behaviour of periodically driven Floquet and MBL systems in the presence of dissipation. Dr Pal brought expertise in MBL, Floquet systems, and quantum information with a focus on numerical methods including Exact Diagonalization (ED) and methods based on tensor networks. Dr Pal also brought expertise on the implementation of quantum information processing in solid states systems, with a view towards quantum technological applications. Dr Bhaseen gave expertise in nonequilibrium quantum many-body systems and field theory techniques, with applications to condensed matter systems and cold atomic gases.
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Reference 2: Time crystals: a review Krzysztof Sacha, Jakub Zakrzewski, Rep. Prog. Phys. 81, 016401 (2018)
Reference 3: The theory of open quantum systems, H. -P. Breuer and F. Petruccione Oxford University Press (2002)
Reference 4: Robustness of Many-Body Localization in the Presence of Dissipation E. Levi, M. Heyl, I. Lesanovsky, and J.P. Garrahan, Physical Review Letters 116, 237203 (2016)
Reference 5: Fate of a discrete time crystal in an open system A. Lazarides and R. Moessner Physical Review B 95, 195135 (2017)