Exotic Phases and Supersymmetry in Quantum Magnets

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Edward O'Brien will study theoretically exotic phases and phase transitions of quantum matter in low dimensions. He will apply both analytical and numerical techniques to these problems. The analytical techniques will include traditional ones arising in statistical mechanics, such as analysing special couplings where the ground state can be found exactly, along with more modern ones such as supersymmetry and conformal field theory. The numerical techniques will include both traditional ones such as exact diagonalisation, and new ones arising in the quantum information world, especially tensor-network methods such as the density-matrix renormalisation group. The initial project will concern the unusual "self-dual ordered" phases arising in quantum spin chains, where ferromagnetically ordered ground states coexist with completely disordered ground states. O'Brien will analyse these phases and the neighbouring tricritical points, and search in particular for lattice supersymmetry. Longer-term goals include analysing similar structure in topologically ordered phases in two dimensions. This work is within the Physical Sciences research theme. The main research area is Condensed matter: magnetism and magnetic materials, while the analytic work has some overlap with Mathematical Physics, and the numerical work with Quantum Optics and Information.There currently are no companies or collaborators outside the University of Oxford involved in this project.