Quantum theory of strong interactions in low dimensional systems

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Anyons emerge as excitations of certain phases of strongly-correlated systems, the epitome of which is the fractional quantum Hall state. Such quasiparticles, which behave as no other particle in nature (i.e. they are neither fermions nor bosons) are of interest for development of topological quantum computation. In this futuristic architecture, qubit are encoded by non-local properties of the system, thus they are robust to local noise and decoherence, and they can be operated upon by braiding anyonic excitations.Some van der Waals 2D materials, such as RuCl3, have recently been shown to host quantum spin liquid phases whose excitations can also behave as anyons. However, evidence remains controversial. Furthermore, there is a general paucity of phases of matter that exhibit these exotic features. Given the interest in quantum technology applications, it is pivotal to investigate from a fundamental perspective how to generate exotic quantum phases hosting (possibly controllable) anyonic excitations on-demand. Recently, the group has shown that twisted Kitaev models (a crude approximation to real materials that capture some of the quantum spin liquid features) can exhibit unprecedented phases of matter. In particular, they can exhibit localisation of anyons in emergent Kagome-like pattern.In this project we want to go beyond the existing model and include features existing in real materials, in particular beyond-Kitaev spin interactions. We aim at doing this with a combination of analytical and numerical techniques, including the role of these interactions via variational methods. The student will therefore derive effective models describing the motion of quasiparticles in the systems under study due to beyond-Kitaev interactions. We will then solve the resulting models and find phase transition points and improve our results of twisted quantum-spin-liquid bilayers. The project thus sits at the intersection between quantum material design and (because of its possible applications) quantum technology.