Quantum Cosmology

We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then present the minisuperspace Wheeler--DeWitt equation and elaborate on the problem of time, the imposition of boundary conditions, the semiclassical approximation, the origin of irreversibility, and singularity avoidance. Restriction is made to quantum geometrodynamics; loop quantum gravity and string theory are discussed in other contributions to this volume.Comment: 29 pages, 9 figures, contribution to "Beyond the Big Bang", ed. by R. Vaas (Springer 2008); typos corrected, reference adde

Density matrix embedding theory for interacting electron-phonon systems

We describe the extension of the density matrix embedding theory (DMET) framework to coupled interacting fermion-boson systems. This provides a frequency-independent, entanglement embedding formalism to treat bulk fermion-boson problems. We illustrate the concepts within the context of the one-dimensional Hubbard-Holstein model, where the phonon bath states are obtained from the Schmidt decomposition of a self-consistently adjusted coherent state. We benchmark our results against accurate density matrix renormalization group calculations