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Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics
Syl Shaw, Rudolf A. Römer
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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) 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. 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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