Quantum Hall physics: Hierarchies and conformal field theory techniques

2016/01/31 by T. H. Hansson, T. H. Hansson, Tony Hansson +8 · 238 citations
Physics and Astronomy · #Conformal field theory #Conformal map #Field (mathematics) #Geometry #Magnetic field #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum field theory #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el

paper · pdf · doi:10.1103/revmodphys.89.025005

published in Reviews of Modern Physics 89(2) (American Physical Society) · added section on experimental status, 59 pages+references, 3 figures

arxiv created 2017/02/14 · openalex created_date 2017/04/07 · openalex publication_date 2017/05/23 · arxiv updated 2017/07/07 · openalex updated_date 2026/08/05

Abstract

The quantum Hall effects by now are recognized as prime examples of the importance of topological considerations in condensed-matter physics. The fractional Quantum Hall effect in particular has proven to display a large number of topologically ordered states that have been classified and understood in terms of hierarchical schemes. This review explains the current understanding of such classifications, with particular emphasis on conformal-field-theory approaches.

Citations

• Fault-tolerant quantum computation by anyons
• Non-Abelian anyons and topological quantum computation

Cited by

• Classifying fusion rules of anyons or SymTFTs: A general algebraic formula for domain wall problems and quantum phase transitions
• Exchange and exclusion in the non-abelian anyon gas
• Giga fine-structure constant in photonic solitons
• Topological Quantum
• Topological phase transitions between bosonic and fermionic quantum Hall states near even-denominator filling factors
• Ideal Optical Flux Lattices
• Higher-order Chern-Simons extensions to QED in 2+1 dimensions
• The numerical case for identifying paired quantum Hall phases by their daughters
• Anyonic analogue of optical Mach-Zehnder interferometer
• Delay Update in determinant quantum Monte Carlo
• Wheeler-DeWitt wavefunctions for 5d BKL dynamics, automorphic L-functions and complex primon gases
• Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators
• Dynamics of Anyon Clusters in Fractional Quantum Hall Fluids
• Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
• Matrix product state representation of quasielectron wave functions
• Effective Abelian theory from a non-Abelian topological order in the ν=2/5 fractional quantum Hall effect
• Three-dimensional topological insulators and bosonization
• Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Non-Abelian fractional quantum Hall state at 3/7-filled Landau level
• Approximate two-body generating Hamiltonian for the particle-hole Pfaffian wave function
• Bosonic quantum Hall states in single-layer two-dimensional optical lattices
• Fractional Quantum Hall Effects

Related

• Ordering the topological order in the fractional quantum Hall effect
• The microscopic origin of the Quantum Hall Effect
• c = 1 conformal field theory and the fractional quantum Hall effect
• The Quantum Hall Effect: Novel Excitations and Broken Symmetries
• Introduction to the Physics of the Quantum Hall Regime