SciPost Phys. Lect. Notes 62 (2022) ·
published 8 September 2022
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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
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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.
