The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

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 …

ITensor is a system for programming tensor network calculations with an interface modeled
on tensor diagram notation, which allows users to focus on the connectivity of a tensor …

Lattice gauge theories, which originated from particle physics in the context of Quantum
Chromodynamics (QCD), provide an important intellectual stimulus to further develop …

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 …

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum
many-body systems in and out of equilibrium. In particular, the one-dimensional matrix …

This is a partly non-technical introduction to selected topics on tensor network methods,
based on several lectures and introductory seminars given on the subject. It should be a …

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying
quantum field theories, and has led to impressive achievements. In particular, it significantly …

The treatment of high‐dimensional problems such as the Schrödinger equation can be
approached by concepts of tensor product approximation. We present general techniques …

During the past 15 years, the density matrix renormalization group (DMRG) has become
increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz …