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

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.