Hybrid Quantum-Classical Methods Model Electron-Phonon Systems, Enabling Study of Holstein Chains and Quenched Disorder
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Understanding how electrons interact with vibrations within materials, particularly in systems with strong electronic interactions and disorder, presents a significant challenge in condensed matter physics.
Heiko Georg Menzler, Suman Mondal, and Fabian Heidrich-Meisner, from the Georg-August-Universität Göttingen and the Max Planck Institute for the Physics of Complex Systems, now address this problem with novel computational techniques. The researchers developed hybrid quantum-classical methods, combining highly accurate quantum simulations with classical descriptions of atomic vibrations, to investigate the behaviour of electrons in materials subject to disorder. This approach allows them to model complex systems and reveals that coupling strongly disordered materials to vibrations promotes electron delocalization, potentially disrupting a phenomenon known as many-body localization and opening new avenues for controlling material properties. This approach efficiently represents the many-body wave function in one dimension while accurately capturing local correlations and spectral properties, allowing for calculations on systems containing up to 100 sites. Researchers demonstrated its effectiveness by applying it to disordered systems coupled to Einstein phonons, revealing the emergence of localisation phenomena and the impact of disorder on the electron-phonon interaction. The results show a clear dependence of the localisation length on both disorder strength and electron-phonon coupling, providing insights into their interplay. This hybrid approach represents a substantial advancement in the computational study of strongly correlated electron and phonon systems, opening new avenues for exploring complex phenomena in condensed matter physics. Holstein Model and Many-Body Localization Studies A comprehensive body of research focuses on the Holstein model, many-body localization (MBL), and quantum-classical dynamics in condensed matter physics and quantum information. The Holstein model describes the interaction between electrons and phonons, serving as a fundamental model for understanding polaron formation and electron transport. Investigations cover disordered Holstein models leading to localisation phenomena, strong coupling regimes, and quantum-classical dynamics using methods like Ehrenfest dynamics. Researchers have extensively employed quantum-classical methods to simulate quantum systems, investigating their accuracy and limitations, particularly for strongly correlated systems. Studies explore thermalisation, ergodicity, and the eigenstate thermalisation hypothesis, alongside prethermalisation and slow dynamics near the MBL transition. This body of work represents a comprehensive overview of research on the Holstein model, many-body localisation, and related topics, highlighting the interplay between these areas and ongoing efforts to understand complex quantum systems. Hybrid Quantum-Classical Simulations of Electron-Phonons Scientists have developed hybrid quantum-classical methods for simulating the time-dependent behaviour of electron-phonon systems, achieving a numerically exact treatment of electronic correlations while modelling optical-phonon degrees of freedom classically. These methods combine time-dependent Lanczos and matrix-product state techniques with the multi-trajectory Ehrenfest approach, offering a powerful new tool for investigating complex material properties. Researchers verified the convergence properties of both methods using a one-dimensional system of interacting spinless fermions, establishing a benchmark against the well-known Holstein chain model. As an application, the team studied the decay of charge density wave order in interacting spinless fermions coupled to Einstein oscillators, introducing quenched disorder to mimic realistic material conditions.
Results demonstrate that coupling disordered systems to classical oscillators induces delocalisation, effectively destabilising many-body localisation, revealing a crucial role for phonons in influencing the electronic behaviour of disordered materials.
Charge Density Wave Decay via New Methods Scientists have developed hybrid quantum-classical methods for simulating the time-dependent behaviour of electron-phonon systems, achieving a numerically exact treatment of electronic correlations while modelling optical-phonon degrees of freedom classically. These methods combine time-dependent Lanczos and matrix-product state techniques with the multi-trajectory Ehrenfest approach, offering a powerful new tool for investigating complex material properties. Researchers verified the convergence properties of both methods using a one-dimensional system of interacting spinless fermions, establishing a benchmark against the well-known Holstein chain model. Applying these methods to the decay of charge density wave order in systems with electronic interactions and quenched disorder, researchers found that coupling to classical phonons promotes delocalisation, effectively destabilising many-body localisation. The dynamics of this decay were found to be subdiffusive, and the rate of decay depends on the strength of the electron-phonon coupling and the electronic interactions. 👉 More information 🗞 Hybrid quantum-classical matrix-product state and Lanczos methods for electron-phonon systems with strong electronic correlations: Application to disordered systems coupled to Einstein phonons 🧠 ArXiv: https://arxiv.org/abs/2512.10899 Tags: