Quantum Field Theory Anomalies in Condensed Matter Physics

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.

arXiv commentLecture notes. 148 pages, 24 figures. v2: Minor typos fixed and some references added

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• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Gravitational Anomalies and Thermal Hall effect in Topological Insulators
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
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• Experimental signature of parity anomaly in semi-magnetic topological insulator
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• Generalized Bloch theorem and chiral transport phenomena
• Axion topological field theory of topological superconductors
• Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
• Conformal Symmetry and Universal Properties of Quantum Hall States
• A New SU(2) Anomaly
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons
• On the cobordism classification of symmetry protected topological phases
• Thermal transport, geometry, and anomalies
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Topological Insulators Avoid the Parity Anomaly
• Hydrodynamics of Euler incompressible fluid and the Fractional Quantum Hall Effect
• Landau levels, Bardeen polynomials and Fermi arcs in Weyl semimetals: the who's who of the chiral anomaly
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Hall Viscosity of Hierarchical Quantum Hall States
• Exact Consequences of the Trace Anomaly in Four Dimensions
• Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor
• On thermal Nieh-Yan anomaly in Weyl superfluids
• Gauge Theories with Ultracold Atoms
• Multipole Expansion in the Quantum Hall Effect
• Thermal equilibration on the edges of topological liquids
• Geometric Induction in Chiral Superconductors
• STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS
• Chiral response in lattice models of Weyl materials
• Bulk-Boundary Correspondence in the Quantum Hall Effect
• Edge Asymptotics of Planar Electron Densities
• On the Electromagnetic Response of Topological Superconductors

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