Contributor info: Prof. Andrea Cappelli

Claudio Bonanno, Andrea Cappelli, Mikhail Kompaniets, Satoshi Okuda, Kay Joerg Wiese

SciPost Phys. 14, 135 (2023) · published 30 May 2023 | Toggle abstract · pdf

The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

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.