Constrained many-body quantum systems

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The recent progress in exploring non-equilibrium dynamics of isolated many-body quantum systems has brought renewed attention on the dynamics and thermalization of closed systems. Generic systems by defauly display ergodic behaviour, at long times reaching a state locally indistinguishable from a thermal one and characterised only by a small number of parameters.At the same time, significant effort has been devoted to studying phenomena far from equilibrium in such systems, often by driving the systems periodically--an example being the discrete time crystals recently observed in experiments. Ergodic systems eventually heat up under these conditions, complicating the observation of such phenomena. It is therefore of interest to understand how to break ergodicity in a robust, non fine-tuned way, providing access to the far from equilibrium regime where new phenomena await discovery.While most work on ergodicity breaking over the last decade has focused on disorder-induced ergodicity breaking in many-body localised (MBL) systems, very recent work has turned to ergodicity breaking in kinetically constrained systems such as appear in Rydberg atom physics. Classically, such constraints amount to forbidding certain dynamical processes; quantum mechanically they map to the vanishing of matrix elements corresponding to such transitions. This project will develop numerical tools and apply them to kinetically constrained models so as to obtain their phenomenology. Based on that, we will then develop approximate analytical tools to provide further insight. These will then be used for preliminary applications to periodically driving such systems as a first step away from equilibrium behaviour.