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My research focusses on the properties of topologically non-trivial systems far from equilibrium.
Topologically distinct systems in equilibrium (at zero temperature) are understood to have ground states which cannot be continuously connected to each other without crossing some phase transition. These distinctions can be captured by topological invariants, e.g. the Chern number for non-interacting fermions in two dimensions. I have been investigating how these invariants behave when a system is driven out of equilibrium by driving, quenching, etc. and how this relates to the topology of the wavefunction.
I am also looking at how these non-equilibrium topological properties relate to physical observables. In particular, we ask whether topological invariants can be measured out of equilibrium, and how they relate to the dynamics of topological edge modes
In Plain English
Generally speaking, `topology' is a branch of mathematics which is concerned with quantities that do not change when the system is smoothly deformed. For example, if you try to stretch and bend a doughnut shape without tearing the shape or gluing parts together, there will always be a hole in the middle, which makes it topologically different from a sphere
Similarly, physical systems can have features which do not change when we deform them. These features will naturally be highly robust to any imperfections that naturally arise in the real world, which makes them both theoretically interesting, and potentially practically useful. In my research, I ask whether these topological features can appear in systems which are dynamic, i.e. time-dependent, and what happens when we drive such systes externally.
- Tenfold Way for Quadratic Lindbladians arXiv: 1908.08834
- Interacting Symmetry-Protected Topological Phases Out of Equilibrium Phys. Rev. Research 1 033204 2019, arXiv: 1908.06875
- Classification of topological insulators and superconductors out of equilibrium Phys. Rev. B 99 075148 2019 (Editors' suggestion), arXiv: 1811.00889
- Slow growth of entanglement and out-of-time-order correlators in integrable disordered systems Phys. Rev. Lett. 122 020603 2019 , arXiv: 1807.06039
- Topology of one dimensional quantum systems out of equilibrium Phys. Rev. Lett. 121 090401 2018 , arXiv: 1804.05756
- Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder Phys. Rev. B 96 241113 2017 , arXiv: 1706.10249
- Topology of quantum systems out of equilibrium Won Nature Reviews Physics Best poster prize at `Conference on quantum dynamics of interacting and disordered systems', Trieste, June 2018
- Entanglement growth and out-of-time-order correlators in integrable disordered systems