Integrable modification of the critical Chalker-Coddington network model

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 f...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2011-10, Vol.84 (14), Article 144201
Main Authors: Ikhlef, Yacine, Fendley, Paul, Cardy, John
Format: Article
Language:English
Subjects:
APPROXIMATIONS
CALCULATION METHODS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
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
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Summary: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.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.84.144201