In this thesis, different wave-function based numerical methods are used to study many-body systems with bosonic degrees of freedom in 1d.
The main focus is on the Holstein model of spinless fermions, where ground-state phases, nonequilibrium dynamics, and thermalization are investigated.
Using matrix-product-state methods for the investigation of such models with electron-phonon coupling poses special numerical challenges.
Local basis optimization, projected purification, and subspace expansion are used to overcome these challenges.
