Exotic Phases and Supersymmetry in Quantum Magnets

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


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.


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Vernier E (2019) Onsager symmetries in $U(1)$ -invariant clock models in Journal of Statistical Mechanics: Theory and Experiment

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509711/1 01/10/2016 30/09/2021
1734484 Studentship EP/N509711/1 01/10/2016 31/03/2020 Edward James O'Brien
Description The Renormalisation Group means that the large-scale properties of complicated systems can often be described very well by those of a far simpler model. By studying a model possessing all of the symmetries of the original system, much can be learnt while only having to deal with a few parameters. We have constructed models in one dimension to study systems with various symmetries. Within these models we have found exotic phases not previously known to be present, implying that general systems with the same symmetries could also possess similar properties in certain regions of their parameter space. In particular, we have found a point in the universality class of the Tricritical Ising model, which is a well-known and much studied continuum field theory, but previously had very few realisations on the lattice. It is also clear from our model how the supersymmetry known to be present in the continuum limit of this model arises naturally from the lattice description, providing insight in this intriguing area.

We have also conducted on exotic phases of matter in 3-state systems. We have found a point in the universality class of the Tricritical Potts model as well a region described by a conformal field theory, which appears to decouple into two different theories, an interesting and, as of yet, not fully understood result.
Exploitation Route There are several interesting areas of our model which could be explored experimentally. In particular, a region with multiple degenerate ground states could prove especially interesting for condensed matter physicists.
Sectors Digital/Communication/Information Technologies (including Software)