Integrable modification of the critical Chalker-Coddington network model

Journal article

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)r×SU(2)r/ SU(2)2r Wess-Zumino-Witten (WZW) coset model for the particular values n=-2cos[π/(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. © 2011 American Physical Society.

Authors: Ikhlef, Y; Fendley, P; Cardy, J

• Journal: Physical Review B - Condensed Matter and Materials Physics
• Volume: 84
• Issue: 14
• Publication date: 2011-10-03
• DOI: 10.1103/PhysRevB.84.144201
• EISSN: 1550-235X
• ISSN: 1098-0121
• Language: English