Quantum Matter in and out of Equilibrium

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Matter -- substance in the world around us -- is "condensed" when its many pieces act in concert. Examples of condensed matter are virtually limitless, since any material is comprised of many individual atoms. The study of condensed matter on a microscopic scale inevitably involves quantum physics -- the laws of nature that apply to small objects such as individual atoms or electrons. Using quantum theory to study condensed matter lies at the heart of our research. Quantum condensed matter theory contains some of the most important, most difficult, and most intriguing questions in modern science. The reason is that the effects of quantum mechanics are all the more complex and surprising when many constituent parts of a large system behave collectively. Unexpected phenomena can "emerge" on large scales that bear no similarity to the microscopic properties. For example, many electrons can collectively "superconduct", carrying electrical current over huge distances with absolutely no loss of energy. An even more spectacular emergent behaviour in some systems is electron "fractionalisation", where the electron effectively has split into pieces!Quantum condensed matter theory is of fundamental academic interest because of the strange and surprising things that occur. It is also essential for the development of a vast range of technologies; it is no exaggeration to say that the computer and communications industries are built upon a foundation of discoveries and understanding in the quantum condensed matter theory of the last century. While our work is mainly academic in nature, our current explorations may very well pave the way for new industries in the years to come. The Oxford quantum condensed matter theory group use modern tools and techniques to unravel the puzzles of quantum condensed matter, to push forward the boundaries of knowledge, and to lay the groundwork for technologies of the future. The research is motivated by the overarching goal of finding structure and patterns in complex quantum systems, and the particular projects are coherent directions united by both specific motivations and methods. The work is summarized by four themes, all at the forefront of modern research:(1) Characterisation and Detection of Topological Matter, a particularly promising type of matter for future quantum technologies, only discovered recently, which so far has defied thorough understanding both theoretically and experimentally. One of its specific features is fractionalization.(2) Non-equilibrium Quantum States of Matter, quantum systems which are not well described by the conventional tools of thermodynamics and statistical mechanics developed in the last century. (3) Geometric Descriptions of Topological Phases -- the best approach to understanding topological matter from Theme (1) often uses a geometrical language. (4) Disorder in Correlated Quantum Matter -- some types of matter appear only in systems with many impurities or irregularities in the arrangements of atoms.The understanding we gain from these explorations will in turn open up new scientific directions.