Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
arXiv:2205.08488 · doi:10.1103/PhysRevB.106.075122
Abstract
Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semi-microscopic description in terms of 1+1 dimensional theories, we discuss the emergence of 2+1 dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge invariant theory and using particle vortex-duality.
arXiv comment32 pages, no figures. v3: typos fixed, refs. updated, minor changes in text and title, published version
References in corpus (40)
- Topological orders and Edge excitations in FQH states
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- Is the Composite Fermion a Dirac Particle?
- The Fractional Quantum Hall effect in an array of quantum wires
- From Luttinger liquid to non-Abelian quantum Hall states
- A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
- Particle-Vortex Duality from 3d Bosonization
- Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
- Lectures on the Quantum Hall Effect
- Wire deconstructionism of two-dimensional topological phases
- Duality between Quantum Critical Points
- Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
- Coupled wire construction of chiral spin liquids
- Particle-vortex duality in topological insulators and superconductors
- Non-Abelian topological insulators from an array of quantum wires
- Chiral Spin Liquids in Arrays of Spin Chains
- Quantum Spin Hall Effect in Strip of Stripes Model
- Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
- Integer and Fractional Quantum Hall Effect in a Strip of Stripes
- Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
- Symmetry and duality in bosonization of two-dimensional Dirac fermions
- Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
- Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
- Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model
- Wire constructions of Abelian topological phases in three or more dimensions
- Fractional topological phases in three-dimensional coupled-wire systems
- From an array of quantum wires to three-dimensional fractional topological insulators
- Coupled wire model of symmetric Majorana surfaces of topological superconductors
- Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
- Coupled-wire constructions: a Luttinger liquid approach to topology
- Quantum Hall Fluids
- Quantum Hall hierarchy from coupled wires
- Two dimensional spin liquids with topological order in an array of quantum wires
- From coupled-wire construction of quantum Hall states to wave functions and hydrodynamics
- Coupled Wire Model of Z4 Orbifold Quantum Hall States
- From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
- Lectures on Dualities in 2+1 Dimensions
- Coupled Wire Models of Interacting Dirac Nodal Superconductors
- Fractional topological insulator precursors in spin-orbit fermion ladders
- Effective Theories for 2+1 Dimensional Non-Abelian Topological Spin Liquids