Data-driven reconstruction of band dispersion and quantum geometry via Koopman dynamical mode decomposition

TL;DR

This paper introduces a data-driven method using Koopman-DMD to reconstruct band structures and quantum geometric properties directly from spatiotemporal data, bypassing explicit Hamiltonian derivation.

Contribution

It establishes a novel framework linking Koopman-DMD with Hamiltonian Floquet-Bloch decomposition for analyzing spectral and topological properties from data.

Findings

Successfully applied to tight-binding models including disordered and Floquet systems

Reconstructed spectral functions, density of states, and localization measures

Inferred quantum geometric and topological invariants from data

Abstract

We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band dispersion and modal dynamics directly from spatiotemporal data, including wavefunctions and observables. This framework establishes a correspondence between Hamiltonian Floquet-Bloch decomposition and Koopman-DMD, whereby the extracted DMD modes encode frequencies, decay or growth rates, spatial profiles and projection weights. These quantities allow the reconstruction of spectral functions, local density of states, and delocalized-to-localized measures such as the inverse participation ratio. Also, these extended DMD modes enable inference of quantum-geometric and topological properties, including the quantum metric, Berry curvature and geometric phases. Applications to prototypical one- and two-dimensional tight-binding models, including disordered Su-Schrieffer-Heeger model and its Floquet and non-Hermitian variants, graphene and Haldane models, demonstrate that Koopman-DMD provides a unified route for the data-driven analysis of wave propagation, localization, and topological phases in condensed matter, photonics, and related fields.