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 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.
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
Center for High Performance Computing Research
Keywords and Phrases
Anderson localization; Critical exponent; Quantum Hall effect
International Standard Serial Number (ISSN)
Article - Journal
© 2021 Elsevier, All rights reserved.
01 Dec 2021
Published online: 24 Apr 2021