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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

Heiko Georg Menzler1,*, Suman Mondal2,*, and Fabian Heidrich-Meisner1

  • *These authors contributed equally to this work.
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Phys. Rev. B 113, 115116 – Published 9 March, 2026

DOI: https://doi.org/10.1103/bn9v-ggzk

Abstract

We present two quantum-classical hybrid methods for simulating the time-dependence of electron-phonon systems that treat electronic correlations numerically exactly and optical-phonon degrees of freedom classically. These are a time-dependent Lanczos and a matrix-product state method, each combined with the multitrajectory Ehrenfest approach. Due to the approximations, reliable results are expected for the adiabatic regime of small phonon frequencies. We discuss the convergence properties of both methods for a system of interacting spinless fermions in one dimension and provide a benchmark for the Holstein chain. As a first application, we study the decay of charge-density wave order in a system of interacting spinless fermions coupled to Einstein oscillators and in the presence of quenched disorder. We investigate the dependence of the relaxation dynamics on the electron-phonon coupling strength and provide numerical evidence that the coupling of strongly disordered systems to classical oscillators leads to delocalization, thus destabilizing the (finite-size) many-body localization in this system.

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Corrections

1 April, 2026

Correction: Reference [21] contained incorrect source information and has been fixed.

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Phys. Rev. B 113, 115116– Published 9 March, 2026
  • Received 17 December 2025
  • Revised 1 February 2026
  • Accepted 6 February 2026
  • Corrected 1 April 2026
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