|dc.description.abstracteng||The emergence of order in materials with strongly-correlated electrons in out-of-equilibrium
situations inspires a lot of new research, both experimental and theoretical. The main goal of
this theoretical research project is to better understand related questions in the dynamics in a
strongly correlated many-body state after a photoexcitation has occured.
Such situations are usually not fully explainable in a mean-field picture nor analytically solvable.
Hence, advanced numerical techniques are necessary. In this work, we investigate non-equilib-
rium situations after photoexcitations. In order to model a hypothetical one-dimensional (1D)
manganite, we chose the 1D Hubbard model with nearest-neighbor interaction and a staggered
magnetic field. The photoexcitation is modeled in two different ways: First we investigate sud-
den, local excitations, and afterwards we study a semi-classical approach by applying the Peierls
substitution, which leads to a time-dependent Hamiltonian.
All simulations are performed with an implementation of the time-dependent density-matrix
renormalization group (DMRG), which is formulated by tensor-network states (TNSs), namely
matrix-product states (MPSs) and matrix-product operators (MPOs). The framework used offers
the possibility that every MPO can be externally described by finite-state machines (FSMs),
hence it is extremely flexible. In this thesis, we explain how to perform exact FSM arithmetics,
and how to compress the resulting FSMs. Based on MPSs and FSMs, a quantum-computer
simulator (QCS) is introduced, which is mainly used as a universal tool for (MPS)-quantum-
From the investigations with the sudden, local excitations, we learned that the electron-electron
interaction is responsible for a rapid relaxation of the magnetic moment of the individual bands.
Nevertheless, this relaxation can be stalled via a stronger magnetic microstructure.
By applying a spin-selective photoexcitation via the Peierls substitution, we are able to induce
a meta-stable charge-density wave (CDW) pattern if a magnetic microstructure is present. For
a small, but finite interaction, we find a decay channel for the doublon-based part of the CDW,
which still leaves a finite pattern. For large interaction, nearly no doublons are created by the
photoexcitation. In the opposite limit, i.e., the non-interacting case, the two spin species are
decoupled. Hence, in both limits the decay channel does not weaken the CDW and we find the
pattern to be stable up to the times we can treat.||de