Physical interactions in quantum many-body systems are typically local: Individual
constituents interact mainly with their few nearest neighbors. This locality of interactions is …

Tensor networks provide extremely powerful tools for the study of complex classical and
quantum many-body problems. Over the past two decades, the increment in the number of …

The density-matrix renormalization group method (DMRG) has established itself over the
last decade as the leading method for the simulation of the statics and dynamics of one …

Matrix-product states have become the de facto standard for the representation of one-
dimensional quantum many body states. During the last few years, numerous new methods …

Interactions in quantum systems can spread initially localized quantum information into the
exponentially many degrees of freedom of the entire system. Understanding this process …

Recent years have seen tremendous progress in the theoretical understanding of quantum
systems driven dissipatively by coupling to different baths at their edges. This was possible …

We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator
entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful …

Enhancing optical nonlinearities so that they become appreciable on the single photon level
and lead to nonclassical light fields has been a central objective in quantum optics for many …

Tensor network methods are taking a central role in modern quantum physics and beyond.
They can provide an efficient approximation to certain classes of quantum states, and the …

The entanglement in operator space is a well established measure for the complexity of the
quantum many-body dynamics. In particular, that of local operators has recently been …