Green's Functions on a Renormalized Lattice: An Improved Method for the Integer Quantum Hall Transition

Author

Martin Puschmann
Thomas Vojta, Missouri University of Science and TechnologyFollow

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.

Recommended Citation

M. Puschmann and T. Vojta, "Green's Functions on a Renormalized Lattice: An Improved Method for the Integer Quantum Hall Transition," Annals of Physics, vol. 435, no. Part 1, article no. 168485, Elsevier, Dec 2021.

The definitive version is available at https://doi.org/10.1016/j.aop.2021.168485

Department(s)

Physics

Research Center/Lab(s)

Center for High Performance Computing Research

Comments

Published online: 24 Apr 2021

Keywords and Phrases

Anderson localization; Critical exponent; Quantum Hall effect

International Standard Serial Number (ISSN)

0003-4916

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Elsevier, All rights reserved.

Publication Date

01 Dec 2021