Integrable modification of the critical Chalker-Coddington network model

Journal Article · Sat Oct 01 04:00:00 EDT 2011 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.84.144201· OSTI ID:21596895

Ikhlef, Yacine; Fendley, Paul; Cardy, John ^[1]

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1. Section Mathematiques, Universite de Geneve 2-4 rue du Lievre, CP 64, SZ-1211 Geneve 4 (Switzerland)

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.

• OSTI ID: 21596895
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 14 Vol. 84; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
CALCULATION METHODS
COMPOSITE MODELS
COMPUTERIZED SIMULATION
DIAGRAMS
FLAVOR MODEL
HALL EFFECT
INFORMATION
LIE GROUPS
MATHEMATICAL MODELS
MODIFICATIONS
PARTICLE MODELS
PHASE DIAGRAMS
QUARK MODEL
SIMULATION
SU GROUPS
SU-2 GROUPS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
TWO-DIMENSIONAL CALCULATIONS