Abstract
The real-space renormalisation group method can be applied to the Chalker–Coddington model of the quantum Hall transition to provide a convenient numerical estimation of the localisation critical exponent, ν. Previous such studies found ν∼2.39 which falls considerably short of the current best estimates by transfer matrix (ν=2.593+0.005−0.006) and exact-diagonalisation studies (ν=2.58(3)). By increasing the amount of data 500 fold we can now measure closer to the critical point and find an improved estimate ν=2.51+0.11−0.11. This deviates only ∼3% from the previous two values and is already better than the ∼7% accuracy of the classical small-cell renormalisation approach from which our method is adapted. We also study a previously proposed mixing of the Chalker–Coddington model with a classical scattering model which is meant to provide a route to understanding why experimental estimates give a lower ν∼2.3. Upon implementing this mixing into our RG unit, we find only further increases to the value of ν.
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