Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators

2015/05/19 by Max A. Metlitski, Ashvin Vishwanath · 3 citations
Mathematics · Physics and Astronomy · #Dirac (video compression format) #Dirac fermion #Duality (order theory) #Electron #Fermion #Mathematics #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #Vortex #cond-mat.mes-hall #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevb.93.245151

published as Phys. Rev. B 93, 245151 (2016) · 14 pages, 3 pages appendices, 1 figure

arxiv created 2015/05/19 · openalex created_date 2016/06/24 · openalex publication_date 2016/06/27 · arxiv updated 2016/07/06 · openalex updated_date 2026/08/06

Abstract

Duality is a powerful theoretical tool whereby the strongly interacting and intractable regime of a theory can be accessed in terms of weakly interacting ``dual'' variables. In condensed matter, this is familiar from the Kramers-Wannier duality of the Ising model, and boson-vortex duality. Here, a duality for another fundamental problem -- Dirac fermions in two spatial dimensions -- is obtained, which provides a new window to the physics of strongly interacting electrons. This leads to unexpected connections between topological insulators in three dimensions and the physics of the half-filled Landau level, including composite fermions and Pfaffian quantum Hall states.

Citations

• Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach
• Periodic table for topological insulators and superconductors
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Classification of topological insulators and superconductors in three spatial dimensions
• Relativity Restored: Dirac Anisotropy inQED3
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Masses and phase structure in the Ginzburg-Landau model
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State

Cited by

• One-dimensional bosonization and the SYK model
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Three-dimensional topological insulators and bosonization