Robust many-body Quantum phenomena through Driving and Dissipation

小学生学习物质的三个阶段：液体、固体和气体。在低温下，这个列表显然是不完整的，因为量子力学原理更明显地决定了材料的性质，导致了大量的新状态，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，我相信……永远不会被推翻。”两个重要的问题出现了：1)假设是有效的，也就是说，所有的系统都趋于平衡吗？ 2)当它们趋于平衡时，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：一些系统不平衡，并且在标准热力学范式之外存在大量新的非平衡相。这一发现是由多体局域相（MBL）的发现引发的，这种相的强无序性阻碍了电荷和能量的平衡，这与热力学的标准假设相反。尽管MBL系统具有革命性，但它们确实在以下意义上稳定下来：如果不受干扰，可观测值在晚些时候稳定下来（是静态的）。令人惊讶的是，通过周期性驱动和无序的结合，人们可以意识到系统既不能稳定也不能平衡！多体局域时间晶体（TCs）就是一个突出的例子：对于几乎任何初始状态，它们的局部可观测值最终以一个周期为底层驱动周期T的整数倍（例如2T）振荡，因此系统自发地打破了时间平移对称性。一个突出的悬而未决的问题是，在一个开放的量子系统中，即一个受环境耗散影响的系统中，这种效应是否具有鲁棒性。第二个问题涉及到强相关系统如何稳定产生耗散，从而使它们走向稳定状态，以及大量输运系数（电导率等）如何依赖于潜在的微观参数，系统如何响应外部耗散，以及输运的哪些特征是普遍和稳健的定量问题。这个领域有很长的历史，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（下文）。我们对新型量子相的进一步了解彻底改变了物质世界。这个项目旨在继续这场革命，扩展我们对非平衡边界的理解，寻找新的强大的——因此可能有用的——量子现象。我们的主要焦点将放在一个鲜为人知的类多体系统，即那些受环境耗散和周期性驱动。我们将在此背景下探索各种现象，最突出的目标是：1)发展耗散存在下时间晶体稳定新概念背后的理论，2)制定量子信息/纠缠传播理论，3)扩展我们的可解耗散模型。我们将4)利用2)中的理论结果来开发新的数值技术，以探测多体系统中与实验相关的晚时间状态。最后，我们将6)将我们的理论进展转化为与其他可能性相关的实验建议：a)耗散-而不是障碍-可以用来增强时间晶体的稳定性，从而提高其实用性的令人兴奋的前景；b)相互作用系统中的奇异输运，如一维量子磁体中的反常自旋扩散；c)仔细评估在实验中发现的时间晶体，特别是在氮空位中心平台。

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.