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

TL;DR

This paper presents an optimized computational approach combining renormalization and recursive Green's functions to study the critical behavior of the integer quantum Hall transition on a lattice, improving accuracy and efficiency.

Contribution

It introduces a novel method integrating renormalization group steps with recursive Green's functions for better simulation of quantum Hall systems.

Findings

Accurate characterization of the critical energy shift.

Inclusion of two irrelevant exponents improves scaling analysis.

Comparison shows enhanced performance over conventional methods.

Abstract

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