Data-driven approximations of topological insulator systems

TL;DR

This paper introduces a data-driven method to construct tight-binding models for topological insulator systems using spectral and topological data, enabling precise replication of their properties.

Contribution

It presents a novel nonlinear least squares approach to derive discrete models from spectral and topological data, improving accuracy for topological insulator systems.

Findings

Accurately reproduces spectral and topological properties of systems

Effective for models like the Su-Schrieffer-Heeger model

Achieves arbitrary precision in model approximation

Abstract

A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. Specifically, spectral and topological data is used to build an appropriate discrete model that accurately replicates these properties. This work is motivated by topological insulator systems that are often described by tight-binding models. The problem is formulated as the minimization of an appropriate residual (objective) function. Given bulk spectral data and a topological index (e.g. winding number), an appropriate discrete model is obtained to arbitrary precision. A nonlinear least squares method is used to determine the coefficients. The effectiveness of the scheme is highlighted against a Schr\"odinger equation with a periodic potential that can be described by the Su-Schrieffer-Heeger model.