Exploring many-body spectral properties of strongly correlated electron-phonon systems via tensor network methods

Recent progress by some of us allowed to push the frontier of the description of bosonic degrees of freedom with tensor network methods. In this work we present an improvement to existing time evolution methods especially aimed for large local Hilbert spaces O(100). With this method we are able to efficiently describe both the local and global dynamic of excitations/quenches allowing us to explore yet uncharted territory of electron phonon coupling. In particular we investigate dynamic properties of the Hubbard-Holstein model. We shed light to the importance of the many-body character of spectral quantities, such as the optical conductivity and discuss the impact of optical pulses acting upon the ground state.