Generalized multifractality at the spin quantum Hall transition

TKM Institutsseminar

Vortragender:

Jonas Karcher

Datum:

16.12.2021 14:00

Ort:

Room 10.01, Bldg. 30.23, Campus South and via Zoom

Zugehörigkeit:

KIT TKM

Gastgeber:

Prof. Dr. Alexander Mirlin

Abstract

Spin quantum Hall (SQH) transition is a superconducting counterpart of the quantum Hall transition. In presence of disorder, scaling of wave function moments exhibits multifractality (MF) at the SQH critical point. The MF at the SQH transition was studied in previous works. In particular, it was found numerically that the MF spectrum exhibits clear (but relatively weak) deviations from parabolicity.
The concept of MF can be extended to a much broader class of local observables built out of wave functions. To reflect this, we introduce the term "generalized MF". In this work, we perform a detailed analytical and numerical study of the generalized MF at the SQH transition. By using the non-linear sigma model formalism, we determine pure-scaling composite operators that correspond to various representations (that can be labelled by Young tableaus or their extension). Further, we perform a "translation" from the field-theory language to that of wave-function correlators. Using the network model of class C, we verify numerically that these correlators exhibit the generalized MF scaling.
Very remarkaby, the numerically determined exponents strongly violate the "generalized parabolicity" (proportionality to the quadratic Casimir invariant). At the same time, the generalized parabolicity can be shown analytically to hold at a 2D localization-transition point if one makes assumptions of the abelian fusion of composite operators and of local conformal invariance of the theory. Since the abelian fusion is verified explicitly, our numerical results point out to a violation of the local conformal invariance at the SQH transition.