The fractional quantum Hall effect: Chern-Simons mapping,duality, Luttinger liquids and the instanton vacuum |
| |
| Institution: | 1. Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands;2. Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4060, USA;1. School of Applied Sciences (Physics), KIIT University, Bhubaneswar 751024, Odisha, India;2. Condensed Matter Physics Group, Physics Enclave, Plot No. – 664/4825, Lane-4A, Shree Vihar, Chandrasekharpur, Po-Patia, Bhubaneswar 751031, Odisha, India;1. Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, WA USA;2. Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia;3. Department of Mathematics, Louisiana State University, Baton Rouge, LA USA;4. Department of Mathematics, Texas A&M University, College Station, TX USA;5. Microsoft Research Station Q and Department of Mathematics, University of California, Santa Barbara, CA USA;1. CERN Theory Department, CH-1211 Geneve 23, Switzerland;2. Institute of Physics, Laboratory for Particle Physics and Cosmology, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland |
| |
| Abstract: | We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We introduce a theory of spatially separated edge modes, find an enlarged dual symmetry and obtain a complete classification of quasiparticle operators and tunneling exponents. The chiral anomaly on the edge is used to obtain unambiguously the Hall conductance. In resolving the problem of counter-flowing edge modes, we find that the long range Coulomb interactions play a fundamental role. In order to set up a theory for arbitrary ν we use the idea of a two-dimensional network of percolating edge modes. We derive an effective, single mode Luttinger liquid theory for tunneling processes into the edge which yields a continuous tunneling exponent 1/ν. The network approach is also used to re-derive the instanton vacuum theory for plateau transitions. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
