The density-matrix renormalization group

U Schollwöck - Reviews of modern physics, 2005 - APS
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient
truncation of the Hilbert space of low-dimensional strongly correlated quantum systems …

The density matrix renormalization group in quantum chemistry

GKL Chan, S Sharma - Annual review of physical chemistry, 2011 - annualreviews.org
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 …

[HTML][HTML] Time-evolution methods for matrix-product states

S Paeckel, T Köhler, A Swoboda, SR Manmana… - Annals of Physics, 2019 - Elsevier
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 ring decomposition

Q Zhao, G Zhou, S Xie, L Zhang, A Cichocki - arXiv preprint arXiv …, 2016 - arxiv.org
Tensor networks have in recent years emerged as the powerful tools for solving the large-
scale optimization problems. One of the most popular tensor network is tensor train (TT) …

The density-matrix renormalization group in the age of matrix product states

U Schollwöck - Annals of physics, 2011 - Elsevier
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 …

Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

H Zhai, HR Larsson, S Lee, ZH Cui, T Zhu… - The Journal of …, 2023 - pubs.aip.org
block2 is an open source framework to implement and perform density matrix
renormalization group and matrix product state algorithms. Out-of-the-box it supports the …

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

F Verstraete, V Murg, JI Cirac - Advances in physics, 2008 - Taylor & Francis
Full article: Matrix product states, projected entangled pair states, and variational
renormalization group methods for quantum spin systems Skip to Main Content Taylor and …

Real-time evolution using the density matrix renormalization group

SR White, AE Feiguin - Physical review letters, 2004 - APS
We describe an extension to the density matrix renormalization group method incorporating
real-time evolution. Its application to transport problems in systems out of equilibrium and …

The kernel polynomial method

A Weiße, G Wellein, A Alvermann, H Fehske - Reviews of modern physics, 2006 - APS
Efficient and stable algorithms for the calculation of spectral quantities and correlation
functions are some of the key tools in computational condensed-matter physics. In this paper …

Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces

AJ Daley, C Kollath, U Schollwöck… - Journal of Statistical …, 2004 - iopscience.iop.org
An algorithm for the simulation of the evolution of slightly entangled quantum states has
been recently proposed as a tool to study time-dependent phenomena in one-dimensional …