A universal fault-tolerant quantum computer that can efficiently solve problems such as
integer factorization and unstructured database search requires millions of qubits with low …

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

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

Metal ions play significant roles in numerous fields including chemistry, geochemistry,
biochemistry, and materials science. With computational tools increasingly becoming …

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 …

Quantum impurity models describe an atom or molecule embedded in a host material with
which it can exchange electrons. They are basic to nanoscience as representations of …

Presenting the physics of the most challenging problems in condensed matter using the
conceptual framework of quantum field theory, this book is of great interest to physicists in …

The density matrix renormalization group is a method that is useful for describing molecules
that have strongly correlated electrons. Here we provide a pedagogical overview of the …

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

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization
group transformation. When applied to the Kondo problem, this numerical renormalization …