Lattice Models of Higher Topological Quantum Field Theories

Lead Research Organisation: University of Oxford
Department Name: Oxford Physics

Abstract

Recent work from a number of Groups (Farins, Martins, Bullaivant n Leeds; Wang and Williamson at Microsoft, Cui at Stanford) has proposed a new type of topological quantum field theory based on what is known as a higher category, or a higher gauge theory. These field theories are based on crossed modules (or G-crossed categories). At the same time, the crossed modules are closely related to symetry protected topological (or enriched) phases, a subject of considerable modern interest. We hope to make the connection to symmetry breaking explicit in these models and how they are related to other topological quantum models, including walker wang models.

This direciton of research is of interest to a wide range of researchers, from mathematicians interested in TQFTs to condensed matter physicsists interested in what sort of matter can exist in real physical systems. From a quantum information perspective, this direction of research can be thought of as potentially new models for quantum memories.

Much of what is known about these model is know from a very abstract mathematical perspective which makes the physical properties of such systems hard to unravel. Obtaining a simple geometric picture (similar to what I did a few years ago with Burnell and von Keyserlingk on earlier Walker-Wang models) will be one of our first tasks.

This project is intended to be somewhat forward looking and adventurous. It will be important for the graduate student to also learn more well-grounded condensed matter physics in order to keep contact with the broader field.

This project falls under the EPSRC Quantum Technologies research area.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513295/1 01/10/2018 30/09/2023
2114104 Studentship EP/R513295/1 01/10/2018 31/03/2022 Joe Charles Huxford