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 offreedom classically. These are a time-dependent Lanczos and a matrix-product state method, eachcombined with the multi-trajectory Ehrenfest approach. Due to the approximations, reliable resultsare expected for the adiabatic regime of small phonon frequencies. We discuss the convergenceproperties of both methods for a system of interacting spinless fermions in one dimension and providea benchmark for the Holstein chain. As a first application, we study the decay of charge densitywave order in a system of interacting spinless fermions coupled to Einstein oscillators and in thepresence of quenched disorder. We investigate the dependence of the relaxation dynamics on theelectron–phonon coupling strength and provide numerical evidence that the coupling of stronglydisordered systems to classical oscillators leads to delocalization, thus destabilizing the (finite-size)many-body localization in this system.