Real-space renormalisation approach to the Chalker–Coddington model revisited: Improved statistics

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, .Previous such studies found ∼ 2.39 which falls considerably short of the current best estimates by transfer matrix ( = 2.593 +0.005 -0.006 ) and exact-diagonalisation studies ( = 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 = 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 ∼ 2.3.Upon implementing this mixing into our RG unit, we find only further increases to the value of .