Integrable modification of the critical Chalker-Coddington network model

Journal Article · Sat Oct 01 00:00:00 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]

---

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, Vol. 84, Issue 14; Other Information: DOI: 10.1103/PhysRevB.84.144201; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

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