Rise and Fall of Anderson Localization by Lattice Vibrations - A Time-Dependent Machine Learning Approach

Aug 3, 2026

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Electron–lattice coupling is central to condensed-matter physics, traditionally treated with the Fröhlich model and perturbative intuition. This work leverages quantum acoustics to view lattice vibrations as waves and uses time-dependent machine learning to classify electron–lattice interaction regimes, exposing a transient localization region where strong lattice motion temporarily traps electronic wavepackets and later releases them as the lattice evolves. The resulting dynamics span the Fröhlich spectrum and suggest routes toward designing materials with tailored electron–lattice properties.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

Introduction

Anderson localization in disordered systems

Conditions for localization in interacting systems

Transient localization and lattice-driven disruption

Fröhlich model and quantum acoustics framework

arXiv :2406 .00042v2 [ cond-mat .str-el ] 30 Jun 2024 Rise and Fall of Anderson Localization by Lattice Vibrations: A Time-Dependent Machine Learning Approach Yoel Zimmermann, 1, 2, ∗ Joonas Keski-Rahkonen,2, 3 Anton M. Graf,3, 4 and Eric J. Heller2, 3,† 1 Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland 2 Department of Physics, Harvard University, Cambridge, MA 02138, USA 3 Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA 4 Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA (Dated: July 2, 2024) The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fr¨ohlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron–lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fr¨ohlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron–lattice properties. I. INTRODUCTION Anderson localization refers to the cessation of diffusive wave propagation in disordered systems [1] . On the historical front, Thouless theoretically posited [2] that at low temperatures, where inelastic processes are minimal, localization would result in higher resistance compared to that expected from ordinary elastic scattering. This insight later spurred the development of the scaling theory of Anderson localization for non-interacting electrons [3] . On the other hand, the conditions facilitating Anderson localization within an interacting system have been found to rely on several factors, including the strength of disorder, the dimensionality of the system [4], the range and type of interactions [5–7], and the time scales of the disorder potential dynamics [8, 9] . The conundrum of whether systems localize or not was recognized early on by researchers like Gogolin [10, 11], Thouless [2], and also Anderson [1, 12] . For instance, the complex interplay between Anderson localization and lattice vibrations is observed in various random metal alloys and other disordered systems, such as crystalline organic semiconductors [13, 14] and halide perovskites [15] . The random fluctuations caused by lattice motion gradually disrupt the quantum interference necessary for electronic state localization, leading to what has been coined transient localization (for capturing the essential aspects, ∗ [yzimmermann@ethz.ch](yzimmermann@ethz.ch)[ ](yzimmermann@ethz.ch)† [eheller@fas.harvard.edu](eheller@fas.harvard.edu) see, e.g., Ref. [9]) . This phenomenon combines aspects of both Anderson localized and itinerant electron systems: Electronic transport is characterized by the successive cycles of localization and delocalization `a la Anderson stemming from lattice vibrations that eventually result in reduced diffusion. Whereas Anderson localization is typically explored within the framework o

FAQs

What does the time-dependent machine learning approach reveal in the electron–lattice dynamics?

It identifies and categorizes distinct interaction regimes and highlights a previously elusive region where electronic motion undergoes transient localization driven by strong lattice vibrations.

How does quantum acoustics differ from the conventional phonon-number picture?

Quantum acoustics treats lattice vibrations as wave-like quantum fields using a coherent-state basis, making phase information and wave dynamics explicit rather than focusing only on phonon numbers.

What is transient localization, and why is it important here?

Transient localization describes a momentary Anderson-like trapping of electronic wavepackets caused by strong dynamical lattice distortions, followed by release as the lattice evolution proceeds, producing reduced diffusion overall.

Aug 3, 2026

Upload by Maeve