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

TL;DR

This paper introduces hybrid quantum-classical methods combining Lanczos and matrix-product state techniques with Ehrenfest dynamics to simulate electron-phonon systems, revealing how classical phonons influence localization.

Contribution

The work develops and benchmarks two hybrid methods for simulating electron-phonon systems, demonstrating their effectiveness in studying disorder and localization effects.

Findings

Hybrid methods accurately simulate electron-phonon dynamics in the adiabatic regime.

Classical phonon coupling can delocalize disordered systems, destabilizing many-body localization.

Benchmark results for the Holstein chain validate the methods' reliability.

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 multi-trajectory 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.