An integrable modification of the critical Chalker-Coddington network model

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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 × SU(2)ᵣ / SU(2)₂ᵣ Wess-Zumino-Witten (WZW) coset model for the particular values n= -2[π/(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.