skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Integrable modification of the critical Chalker-Coddington network model

Abstract

We consider the Chalker-Coddington network model for the integer quantum Hall effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models with two loop flavors. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra and parameterized by the loop fugacity n. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-gas theory, whereas the other two branches (3,4) couple the two loop flavors, and relate to an SU(2){sub r}xSU(2){sub r}/SU(2){sub 2r} Wess-Zumino-Witten (WZW) coset model for the particular values n=-2cos[{pi}/(r+2)], where r is a positive integer. The truncated Chalker-Coddington model is the n=0 point of branch 4. By numerical diagonalization, we find that its universality class is neither an analytic continuation of the WZW coset nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.

Authors:
; ;  [1];  [2];  [3]
  1. Section Mathematiques, Universite de Geneve 2-4 rue du Lievre, CP 64, SZ-1211 Geneve 4 (Switzerland)
  2. (United States)
  3. (United Kingdom) and All Souls College, Oxford (United Kingdom)
Publication Date:
OSTI Identifier:
21596895
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 84; Journal Issue: 14; Other Information: DOI: 10.1103/PhysRevB.84.144201; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; FLAVOR MODEL; HALL EFFECT; MODIFICATIONS; PHASE DIAGRAMS; SU-2 GROUPS; SUPERSYMMETRY; TWO-DIMENSIONAL CALCULATIONS; CALCULATION METHODS; COMPOSITE MODELS; DIAGRAMS; INFORMATION; LIE GROUPS; MATHEMATICAL MODELS; PARTICLE MODELS; QUARK MODEL; SIMULATION; SU GROUPS; SYMMETRY; SYMMETRY GROUPS

Citation Formats

Ikhlef, Yacine, Fendley, Paul, Cardy, John, Microsoft Research, Station Q, University of California Santa Barbara, California 93106, USA and Department of Physics, University of Virginia Charlottesville, Virginia 22904-4714, and Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP. Integrable modification of the critical Chalker-Coddington network model. United States: N. p., 2011. Web. doi:10.1103/PHYSREVB.84.144201.
Ikhlef, Yacine, Fendley, Paul, Cardy, John, Microsoft Research, Station Q, University of California Santa Barbara, California 93106, USA and Department of Physics, University of Virginia Charlottesville, Virginia 22904-4714, & Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP. Integrable modification of the critical Chalker-Coddington network model. United States. doi:10.1103/PHYSREVB.84.144201.
Ikhlef, Yacine, Fendley, Paul, Cardy, John, Microsoft Research, Station Q, University of California Santa Barbara, California 93106, USA and Department of Physics, University of Virginia Charlottesville, Virginia 22904-4714, and Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP. Sat . "Integrable modification of the critical Chalker-Coddington network model". United States. doi:10.1103/PHYSREVB.84.144201.
@article{osti_21596895,
title = {Integrable modification of the critical Chalker-Coddington network model},
author = {Ikhlef, Yacine and Fendley, Paul and Cardy, John and Microsoft Research, Station Q, University of California Santa Barbara, California 93106, USA and Department of Physics, University of Virginia Charlottesville, Virginia 22904-4714 and Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP},
abstractNote = {We consider the Chalker-Coddington network model for the integer quantum Hall effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models with two loop flavors. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra and parameterized by the loop fugacity n. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-gas theory, whereas the other two branches (3,4) couple the two loop flavors, and relate to an SU(2){sub r}xSU(2){sub r}/SU(2){sub 2r} Wess-Zumino-Witten (WZW) coset model for the particular values n=-2cos[{pi}/(r+2)], where r is a positive integer. The truncated Chalker-Coddington model is the n=0 point of branch 4. By numerical diagonalization, we find that its universality class is neither an analytic continuation of the WZW coset nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.},
doi = {10.1103/PHYSREVB.84.144201},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 14,
volume = 84,
place = {United States},
year = {2011},
month = {10}
}