Constrained many-body quantum systems

孤立多体量子系统非平衡动力学研究的最新进展使人们重新关注封闭系统的动力学和热化。一般系统通过defauly显示遍历行为，在很长一段时间内达到一个状态，局部无法区分从一个热的，其特点是只有少数参数，同时，显着的努力一直致力于研究远离平衡的现象，在这样的系统，往往是通过驱动系统周期性-一个例子是离散的时间晶体最近在实验中观察到。各态历经系统最终会在这些条件下升温，使对此类现象的观察变得复杂。因此，了解如何以一种稳健的、非微调的方式打破遍历性是一个有趣的问题，它提供了一种进入远离平衡态的途径，在那里新的现象等待着发现。虽然过去十年中关于遍历性打破的大多数工作都集中在多体局域（MBL）系统中无序诱导的遍历性打破上，最近的工作已经转向在动力学约束系统中的遍历性破缺，例如出现在Rydberg原子物理学中。经典上，这样的限制等于禁止某些动力学过程;量子力学上，它们映射到对应于这种转变的矩阵元素的消失。本计画将发展数值工具，并将其应用于动力学约束模型，以获得其现象学。在此基础上，我们将开发近似分析工具，以提供进一步的见解。然后，这些将用于初步应用，以周期性地驱动这些系统，作为远离平衡行为的第一步。

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.