Hamiltonian transformation for accurate and efficient band structure interpolation

TL;DR

The paper introduces the Hamiltonian transformation (HT) method, which significantly improves the accuracy and efficiency of band structure interpolation, especially for complex systems with entangled or topological bands.

Contribution

The novel HT framework localizes the Hamiltonian more effectively than Wannier interpolation, providing higher accuracy and faster computation without complex optimization.

Findings

HT achieves up to two orders of magnitude greater accuracy for entangled bands.

HT offers significant computational speedups over traditional methods.

High-throughput calculations verify HT's robustness and precision.

Abstract

Electronic band structure is a cornerstone of condensed matter physics and materials science. Conventional methods like Wannier interpolation (WI), which are commonly used to interpolate band structures onto dense k-point grids, often encounter difficulties with complex systems, such as those involving entangled bands or topological obstructions. We introduce the Hamiltonian transformation (HT) method, a novel framework that enhances interpolation accuracy by localizing the Hamiltonian. Using a pre-optimized transformation, HT produces a far more localized Hamiltonian than WI-SCDM (where Wannier functions are generated via the selected columns of the density matrix projection), achieving up to two orders of magnitude greater accuracy for entangled bands. Although HT utilizes a slightly larger, nonlocal numerical basis set, its construction is rapid and requires no optimization, resulting in significant computational speedups. These features make HT a more precise, efficient, and robust alternative to WI-SCDM for band structure interpolation, as verified by high-throughput calculations.