Systems of interacting particles can display a variety of emergent cooperative phenomena that cannot be understood from their microscopic details. Usually, the study of this type of "condensed matter" builds on two key principles, namely (i) that most situations can be understood by approximately treating the constituents (such as electrons, atoms, or molecules) as weakly interacting; and (ii) that the assumption of thermal equilibrium provides a powerful way to capture the properties of complex systems using simple statistical tools.
I'm interested in what happens when quantum systems are so strongly interacting, or so dramatically disturbed from equilibrium, that these guiding principles break down. A new set of analytical and computational ideas is therefore required to fully understand the behaviour of such systems, and to explore their properties. Besides their great fundamental interest, many of the new phenomena displayed in these extreme regimes could have many important applications. Insights into weakly-correlated, equilibrium systems fueled the technological revolution of the second half of the twentieth century; what new and unexpected benefits might we accrue from understanding their more complex cousin
On a technical level, my research is centred around two primary themes. The first is the interplay of crystal symmetries with strong correlations and topological effects, and the new states of matter that can emerge as a consequence, in settings such as correlated insulators, topological semimetals, and two-dimensional quantum Hall systems. The second is the dynamics of far-from-equilibrium systems, with a particular focus on many-body localized phases, the many-body localization phase transition, and unconventional transport mechanisms. Both have substantial and increasing benefit from making contact with ideas from quantum information, particularly as it relates to entanglement and measurement. I have a strong interest in working with experimental groups; recent collaborations include those with the groups of Ali Yazdani (Princeton), Amalia Coldea (Oxford), David Weld (UCSB), and Radu Coldea (Oxford).
My research is supported by the Horizon 2020 Program of the European Research Council via a Starting Grant focused on Topological Matter and Crystalline Symmetries [Grant No. 804213-TMCS] and by a UK Engineering and Physical Sciences Research Council grant to the Oxford Condensed Matter Theory group on Coherent Many-Body Quantum States of Matter [EP/S020527/1].