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Fast Fourier-Chebyshev Approach to Real-Space Simulations of the Kubo Formula.

Santiago Giménez de Castro^1,2, João M Viana Parente Lopes³, Aires Ferreira⁴

¹School of Engineering, Mackenzie Presbyterian University, São Paulo - 01302-907, Brazil.

Physical Review Letters

|March 1, 2024

Summary

We developed a hybrid algorithm combining Chebyshev expansions and divide-and-conquer methods to accurately study large 2D lattice models. This approach enables precise calculation of transport properties in complex systems with quenched disorder.

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Area of Science:

Condensed Matter Physics
Computational Physics

Background:

The Kubo formula is essential for understanding near-equilibrium transport phenomena.
Applying Kubo's linear-response theory to large systems is computationally challenging.
Existing algorithms struggle with scalability beyond one spatial dimension.

Purpose of the Study:

To develop a general, accurate, and scalable numerical framework for studying large systems.
To overcome the limitations of current algorithms in applying linear-response theory.
To enable the study of transport phenomena in previously inaccessible regimes.

Main Methods:

A hybrid algorithm combining Chebyshev expansions and divide-and-conquer methods.
Numerical calculation of two-terminal conductance and bulk conductivity tensor.
Application to 2D lattice models exceeding 10^7 sites.

Main Results:

Accurate calculation of transport properties for large 2D lattice models.
Efficient sampling of microscopic information using billions of Chebyshev moments.
Resolution of linear-response properties in systems with quenched disorder.

Conclusions:

The proposed hybrid algorithm provides a powerful tool for studying complex transport phenomena.
This framework significantly advances the ability to analyze large-scale condensed matter systems.
Opens new avenues for research in transport phenomena under challenging conditions.