Quantum spin liquids are exotic phases of matter with long-range entanglement, which allows electrons in the material to separate their electric charge and spin into two independent particles. Some of these systems are also topologically ordered, in which these particles go beyond the usual split between bosons and fermions to realise anyonic statistics. While field theory predicts an abundance of such topologically ordered systems, they have been challenging to realise in microscopic models: most of these favour simpler spin liquids or the length scale for topological order is too large for most numerical methods.

In this project, you will explore the origin of this discrepancy in the field theories that describe quantum spin liquids. In these, the particles carrying spin are coupled to a number of emergent gauge fields: realising topological order requires all of these to be suppressed through the Anderson-Higgs mechanism, similar to how superconductors do not allow magnetic flux to enter them. While this happens generically, it is plausible that some gauge fields are more weakly suppressed than others, able to survive over large length scales and to mask the eventual topological order. The bulk of the project will consist of developing analytical field-theory methods to describe this mechanism; you will also implement its results computationally to study a few models of experimental interest in more detail.

How to apply

If you are interested in this project, please email me and tell me about why you are interested in the project and any relevant background in condensed matter you may have.

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