Green’s functions on a renormalized lattice: An improved method for the integer quantum Hall transition

We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step reduce the sparseness of original problem with recursive Green’s function method. apply this framework investigate critical behavior integer quantum Hall transition Hamiltonian defined simple square lattice. In addition, we employ improved scaling analysis that includes two irrelevant exponents characterize shift energy as well corrections dimensionless Lyapunov exponent. compare our findings results conventional implementation method, and put them into broader perspective in view recent development field.