Contributor info: Prof. Hans Hansson

Thors Hans Hansson, Rodrigo Arouca, Thomas Klein Kvorning

SciPost Phys. 18, 197 (2025) · published 19 June 2025 | Toggle abstract · pdf

We revisit an argument, originally given by Kivelson and Roček, for why the existence of fractional charge necessarily implies fractional statistics. In doing so, we resolve a contradiction in the original argument, and in the case of a $\nu = 1/m$ Laughlin holes, we also show that the standard relation between fractional charge and statistics is necessary by an argument based on a t'Hooft anomaly in a one-form global $\mathcal{Z}_m$ symmetry.

R. Arouca, Andrea Cappelli, T. H. Hansson

SciPost Phys. Lect. Notes 62 (2022) · published 8 September 2022 | Toggle abstract · pdf

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.

Yoran Tournois, Maria Hermanns, Thors Hans Hansson

SciPost Phys. 8, 079 (2020) · published 18 May 2020 | Toggle abstract · pdf

We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.