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PhD student Syl Shaw and supervisor Rudo Roemer apply the real-space renormalisation group method to the Chalker–Coddington model of the quantum Hall transition. This approach provides a convenient numerical estimation of the localisation critical exponent, ν. Previous such studies found ν=2.39 which falls considerably short of the current best estimates by transfer matrix (2.593) and exact-diagonalisation studies (2.58). By increasing the amount of data 500 fold they can now measure closer to the critical point and find an improved estimate 2.51. This deviates only 3% from the previous two values and is already better than the 7% accuracy of the classical small-cell renormalisation approach from which their method is adapted.

Blending ordering within an uncorrelated disorder potential in families of 3D Lieb lattices preserves the macroscopic degeneracy of compact localized states and yields unconventional combinations of localized and delocalized phases—as shown in Liu et al. (Phys Rev B 106:214204, 2022). Danieli, Liu and Roemer proceed to reintroduce translation invariance in the system by further ordering the disorder, and discuss the spectral structure and eigenstates features of the resulting perturbed lattices. This strategy, herewith implemented in the 3D Lieb lattice, highlights order restoration as experimental pathway to engineer spectral and states features in disordered lattice structures in the pursuit of quantum storage and memory applications.

Areej Aljaghwani, a 2^nd year PhD student from Maksym Myronov’s Semiconductors Research Group was awarded second place in the Phil Buckle Research Communication Competition held during the UK Semiconductors Conference in July 2024.