Pushing the limit of quantum transport simulations

2019/06/21 by Mathieu Istas, Christoph Groth, Xavier Waintal
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Graphene research and applications #Invariant (physics) #Limit (mathematics) #Limit set #Mathematical analysis #Mathematics #Physics #Programming language #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Set (abstract data type) #Statistical physics #Theoretical computer science #Theoretical physics #Thermodynamic limit #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevresearch.1.033188

published as Phys. Rev. Research 1, 033188 (2019) · 20 pages, 13 figures

arxiv created 2019/06/21 · openalex publication_date 2019/12/19 · arxiv updated 2019/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper presents a set of algorithms for a restricted family of systems that are mostly invariant by translations. The authors show that these systems can be handled directly in the thermodynamic limit and that they encompass many situations of practical interest such as relatively clean surfaces or very large electrodes. These algorithms are particularly useful for the study of topological materials.

Citations

• Green’s function technique for studying electron flow in two-dimensional mesoscopic samples
• Low-temperature Lanczos method for strongly correlated systems
• The Kernel Polynomial Method
• Landauer formula for the current through an interacting electron region
• Knitting algorithm for calculating Green functions in quantum systems
• Quasiparticle scattering and local density of states in thed-density-wave phase
• Topological Insulators
• Discovery of a Weyl fermion semimetal and topological Fermi arcs
• Linear Scaling Quantum Transport Methodologies
• Quantum Theory of Many Particle Systems