An 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 flavours. 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 parameterised 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 flavours, and relate to an $SU(2{)}_r\times SU(2{)}_r/SU(2{)}_{2r}$ Wess-Zumino-Witten (WZW) coset model for the particular values $n=-2\cos [\pi /(r+2)]$ where $r$ is a positive integer. The truncated Chalker-Coddington model is the $n=0$ point of branch 4. By numerical diagonalisation, 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.

34 pages, 18 figures, 3 appendices

References in corpus (4)

• Critical exponent for the quantum Hall transition
• Discretely Holomorphic Parafermions and Integrable Loop Models
• Loop models and their critical points
• Worm Monte Carlo study of the honeycomb-lattice loop model

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• Dilute oriented loop models
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• On truncations of the Chalker-Coddington model
• Phase diagram and the strong-coupling fixed point in the disordered O(n) loop model
• Logarithmic Correlations in Quantum Hall Plateau Transitions
• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models