Exploring the fuzzy nature of quantum criticality

This PhD research project explores quantum criticality and topologically enriched critical points using fuzzy-sphere regularisation. From the boiling of water to the birth of the universe, continuous phase transitions reveal nature's ability to organise itself in strikingly universal ways. At these critical points, microscopic details are washed away and systems display scale invariance, emergent collective excitations, and mathematical elegance captured by conformal field theories. Building on recent breakthroughs in fuzzy sphere non-commutative geometry born from quantum Hall effect physics, this project will develop and apply advanced numerical techniques including exact diagonalisation, density-matrix renormalisation group, and conformal perturbation theory to extract operator spectra, entanglement signatures, and universal quantities. The research is directly motivated by quantum Hall bilayer experiments in semiconductor heterostructures and graphene, where similar Landau-level physics and interlayer couplings can be realised. The project offers full academic fees plus a tax-free maintenance grant at the standard UKRI rate (£20,780 in 2025/26) for 3.5 years through competitive EPSRC Doctoral Landscape Award or School of Physics & Astronomy Studentship. Only UK applicants are eligible for this opportunity.