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, 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.