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

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.