This paper reviews recent experimental and theoretical progress concerning many-body
phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling …

Originally developed in the context of condensed-matter physics and based on
renormalization group ideas, tensor networks have been revived thanks to quantum …

Controllable, coherent many-body systems can provide insights into the fundamental
properties of quantum matter, enable the realization of new quantum phases and could …

The challenge posed by the many-body problem in quantum physics originates from the
difficulty of describing the nontrivial correlations encoded in the exponential complexity 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 …

One of the key applications for quantum computers will be the simulation of other quantum
systems that arise in chemistry, materials science, etc., in order to accelerate the process of …

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

Statistical mechanics provides a framework for describing the physics of large, complex
many-body systems using only a few macroscopic parameters to determine the state of the …

We review the conformal field theory approach to entanglement entropy in 1+ 1 dimensions.
We show how to apply these methods to the calculation of the entanglement entropy of a …