Robust many-body Quantum phenomena through Driving and Dissipation

小学生学习物质的三种状态：液体、固体和气体。这个列表在低温下是不完整的，量子力学原理更显着地决定材料性质，导致过多的新状态，包括超导体和拓扑相，其中许多具有深远的实际应用。对相的理论研究已经隐含地假设所有这样的系统都达到热力学平衡。这个看似坚实的假设是所有热力学的基础，爱因斯坦曾经说过：“这是唯一具有普遍内容的物理理论，我确信......永远不会被推翻”。两个重要的问题出现了：1）是假设有效，即，所有的系统都趋向于平衡吗？2）当它们趋向于平衡时，它们是如何达到平衡的？“不”是对第一个问题的令人震惊的回答：有些系统不平衡，并且在标准热力学范式之外存在许多新的非平衡相。这一认识是由多体局部化（MBL）相的发现引发的，对于多体局部化相，强烈的无序阻止了平衡，例如，电荷和能量，这与热力学的标准假设相反。MBL系统是革命性的，它们确实在以下意义上解决了问题：不受干扰，可观测量在后期解决（静态）。令人惊讶的是，通过周期性驱动和无序的结合，人们可以实现既无法平衡又无法稳定的系统！多体局域时间晶体（TC）是一个突出的例子：对于几乎任何初始状态，它们的局部可观测量最终都会以整数倍的周期振荡（例如，2 T），因此系统自发地破坏时间平移对称性。一个突出的开放问题是，这种效应在开放量子系统中是否具有鲁棒性，即，一种是环境耗散。第二个问题是关于强相关的系统是如何稳定的产生耗散，使它们趋向稳定状态，以及如何定量的问题，散装运输系数（电导率等）。取决于基本的微观参数，系统如何响应外部耗散，以及传输的哪些特征是普遍和鲁棒的。这一领域有着悠久的历史，很少有受控的结果，并且具有重要的实际意义：进一步的进展将有助于寻找具有特定输运性质的新材料，并澄清现有的实验问题（见下文）。我们对新量子相的理解的增加彻底改变了物质世界。该项目旨在继续革命，扩展我们对非平衡前沿的理解，寻找新的强大的-因此可能有用的-量子现象。我们的主要重点将是对一类知之甚少的多体系统，即那些受环境耗散和周期性驱动。我们将在这种环境中探索各种现象，最突出的目标是：1）发展时间晶体在耗散存在下稳定的新概念背后的理论，2）制定量子信息/纠缠传播理论，3）扩展我们的可解模型的威望。我们将4）使用我们的理论结果2）发展新的数值技术，能够探测实验相关的多体系统的晚时间制度。最后，我们将把我们的理论进展转化为实验建议，其中包括：a）令人兴奋的前景，即耗散--而不是一个障碍--可以用来提高时间晶体的稳定性，从而提高其实际效用; B）相互作用系统中的奇异输运，例如，1D量子磁体中的异常自旋扩散; c）对实验中声称的时间晶体目击事件进行仔细评估，特别是在氮空位中心平台中。

Schoolchildren learn of three phases of matter: Liquid, solid and gas. This list is glaringly incomplete at low temperatures where quantum mechanical principles more markedly determine material properties, leading to a plethora of new states including superconductors and topological phases, many of which have profound practical applications. The theoretical search for phases has implicitly assumed that all such systems come to thermodynamic equilibrium. This seemingly solid assumption underlies all thermodynamics, of which Einstein once said: "It is the only physical theory of universal content, which I am convinced...will never be overthrown". Two important questions arise: 1) is the assumption valid, i.e., do all systems tend to equilibrium and 2) when they do, how do they get there? "No" is the shocking answer to the first question: some systems do not equilibrate, and a host of new non-equilibrium phases exist beyond the standard thermodynamic paradigm. The realisation was sparked by the discovery of many-body localised (MBL) phases, for which strong disorder prevents the equilibration of, e.g., charge and energy, contrary to the standard assumptions of thermodynamics. As revolutionary as MBL systems are, they do settle in the following sense: left undisturbed, observables settle (are static) at late times. Astonishingly, through a combination of both periodic driving and disorder, one can realise systems that robustly both fail to equilibrate and settle! Many-body localised time crystals (TCs) are a prominent example: for almost any initial state, their local observables eventually oscillate with a period that is an integer multiple (e.g., 2T) of the underlying driving period T, hence the system spontaneously breaks time translation symmetry. A prominent open question is whether the effect can be robust in an open quantum system, i.e., one subject to environmental dissipation. The second question concerns how strongly correlated systems that do settle generate the dissipation that drives them towards a steady state, as well as quantitative questions of how bulk transport coefficients (conductivity, etc.) depend on the underlying microscopic parameters, how systems respond to external dissipation, and what features of transport are universal and robust. This field has a long history, few controlled results, and is of great practical importance: further progress will aid in the search for new materials with specified transport properties, and clarify existing experimental questions (below). Our increased understanding of novel quantum phases revolutionised the material world. This project aims to continue the revolution, extending our understanding of the non-equilibrium frontier, searching for new robust---and hence potentially useful---quantum phenomena. Our primary focus will be on a poorly understood class of many-body systems, namely those subject to both environmental dissipation and periodic driving. We will explore various phenomena in this setting, most prominently aiming to: 1) develop the theory behind a new notion of time crystal stable in the presence of dissipation, 2) formulate a theory of quantum information/entanglement spreading and 3) expand our cachet of solvable models with dissipation. We will 4) use our theoretical results in 2) to develop new numerical techniques able to probe the experimentally relevant late time regimes in many-body systems. Finally, we will 6) transform our theoretical progress into experimental proposals pertaining to, amongst other possibilities: a) the exciting prospect that dissipation---rather than being an impediment---can be used to enhance the stability, and hence practical utility, of time crystals; b) exotic transport in interacting systems, e.g., anomalous spin diffusion in 1D quantum magnets; c) a careful assessment of claimed sightings of time crystals in experiments, particularly in Nitrogen vacancy centre platforms.