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

Lead Research Organisation: Royal Holloway, University of London
Department Name: Physics


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.


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Castelnovo C (2012) Topological quantum glassiness in Philosophical Magazine

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Castelnovo C (2011) Debye-Hückel theory for spin ice at low temperature in Physical Review B

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Castelnovo C (2012) Spin Ice, Fractionalization, and Topological Order in Annual Review of Condensed Matter Physics

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Castelnovo C (2013) Negativity and topological order in the toric code in Physical Review A

Related Projects

Project Reference Relationship Related To Start End Award Value
EP/G049394/1 01/10/2009 01/09/2010 £249,514
EP/G049394/2 Transfer EP/G049394/1 01/09/2010 30/09/2012 £172,518
Description my research improved our fundamental understanding of new phases of matter, topological order, and fractionalised excitations. For instance, I contributed to the experimental confirmation of magnetic monopole excitations in spin ice materials and how they affect the behaviour of these systems. I also investigated relaxation time time scales in systems with topological order and how they relate to the protection of quantum information from external perturbations.
Exploitation Route my results contribute to our general understanding of topologically ordered systems and systems beyong a Landau-Ginzburg description in general. Building upon these results it will become eventually possible to develop an overall framework for the study of these systems that improves our understanding and our predictive power. Some of these systems have been speculated to have potential technological impacts. A fundamental understanding is the basis to verify and deliver this impact. Specifically, spin ice materials have been proposed to be useful in the IT industry for novel magnetic circuits and magnetic memories. Furthermore, their large magnetic moments and lack of order down to very low temperature makes them candidate materials for solid state refrigeration (less wasteful than He-based regfrigeration). Finally, quantum topological order has been proposed as a potential route towards quantum computing, and understanding its response to perturbations is of paramount importance in this context, which my results directly contributed to.
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