Quantum Field Theory Anomalies in Condensed Matter Physics
arXiv:2204.02158 · doi:10.21468/SciPostPhysLectNotes.62
Abstract
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.
Lecture notes. 148 pages, 24 figures. v2: Minor typos fixed and some references added
References in corpus (13)
- Classification of topological insulators and superconductors in three spatial dimensions
- The Chiral Magnetic Effect
- Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
- Dirac materials
- Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals
- Choreographed entangle dances: topological states of quantum matter
- Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
- Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
- Axion topological field theory of topological superconductors
- Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
- Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons
- Gauge Theories with Ultracold Atoms
- Chiral response in lattice models of Weyl materials
Cited by in corpus (15)
- An Introduction to Higher-Form Symmetries
- Entanglement asymmetry in the critical XXZ spin chain
- Boundary Modes in the Chamon Model
- Anomalous geometric transport signatures of topological Euler class
- Chiral Meissner effect in time-reversal invariant Weyl superconductors
- Thermodynamics and entanglement entropy of the non-Hermitian SSH model
- Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
- Tunable chiral anomalies and coherent transport on a honeycomb lattice
- On a Solution to the Dirac Equation with a Triangular Potential Well
- Non-Hermitian chiral anomalies in interacting systems
- Chiral vortex-line liquid of three-dimensional interacting Bose systems with moat dispersion
- Anomalies of global symmetries on the lattice
- On the relation between fractional charge and statistics
- Chiral Anomaly Induced Transverse Planar Transport Phenomena in Three Dimensional Spin-Orbit Coupled Metals
- The Lattice Schwinger Model and Its Quantum Simulation