Phase-ordering kinetics and defect dynamics beyond the Landau-Ginzburg description

理解有序如何在相变中出现，以及相应缺陷的行为，长期以来一直是凝聚态物理和宇宙学等不同领域的兴趣所在。然而，到目前为止，大多数工作都是关于相变的，这些相变允许用局部顺序参数进行朗道-金兹堡（LG）描述。近年来，许多理论模型和实验系统的发现都脱离了LG范式。例如，在量子霍尔系统中，拓扑秩序在低温下表现为一种突现的对称性，而不是破缺的对称性，并且它不能被局部可观测到。在不稳定的磁体中，比如钛酸钬和镝的稀土，在非常低的温度下仍然存在大量的熵。系统仍然是无序的，但与高温下的方式不同：低温下的无序相实际上被赋予了一种紧急（规范）对称性，非常类似于螺线线磁场。在拓扑有序的情况下，这种低温阶段不允许立即的LG描述，并且需要开发新的技术来研究其性质。缺乏朗道-金兹堡描述，相序动力学的传统方法的基础不再适用。这项提议的目的是填补这一空白，并研究秩序是如何在这些新的、奇异的物质相中出现的，以及这如何反映在其缺陷的动力学中。从具体的案例研究开始，包括经典和量子系统，该项目将首先关注解决该领域的突出问题。例如，理解最近在受挫磁材料实验中观察到的非常规弛豫和响应特性；以及研究拓扑量子计算中的特征时间尺度，其中的准备、保护和编织操作问题与拓扑缺陷的动力学密切相关。一旦开发出足够的系统特定知识体系，该项目的优先事项将转向为这类系统开发相顺序动力学的综合框架，这是目前文献中缺失的。

Understanding how order emerges across a phase transition, and the behaviour of the corresponding defects, have long been of interest in fields as diverse as condensed matter physics and cosmology. Most of the work to date, however, is concerned with phase transitions that allow for a Landau-Ginzburg (LG) description in terms of a local order parameter. Recent years have witnessed the discovery of a wide range of theoretical models and experimental systems that escape the LG paradigm. For example, in quantum Hall systems, topological order appears as an emergent -- rather than broken -- symmetry at low temperatures, and it cannot be detected by local observables. In frustrated magnets, such as rare earth titanates of Holmium and Dysprosium, an extensive entropy survives down to very low temperatures. The system remains disordered, yet not in the same way as at high temperature: the disordered phase at low temperatures is in fact endowed with an emergent (gauge) symmetry, very much akin to the one of a solenoidal magnetic field. As in the case of topological order, this low temperature phase does not allow for an immediate LG description, and new techniques need be developed in order to investigate its properties. Lacking a Landau-Ginzburg description, the very bases of a conventional approach to phase-ordering kinetics no longer apply. The aim of this proposal is to fill in this gap, and investigate how order emerges in these new, exotic phases of matter, and how this reflects in the dynamics of its defects. Starting from specific case studies, encompassing both classical and quantum systems, this project will be first concerned with addressing outstanding questions in the field. For example, understanding the non-conventional relaxation and response properties recently observed in experiments on frustrated magnetic materials; as well as investigating the characteristic time scales in topological quantum computing, where issues of preparation, protection, and braiding operations are closely related to the dynamics of topological defects. Once a sufficient body of system-specific knowledge has been developed, the priority of the project will shift towards developing a comprehensive framework of phase-ordering kinetics for this type of systems, which is currently missing in the literature.