Tensor networks for dimensionality reduction and large-scale optimization: Part 2 applications and future perspectives

A Cichocki, AH Phan, Q Zhao, N Lee… - … and Trends® in …, 2017 - nowpublishers.com
Part 2 of this monograph builds on the introduction to tensor networks and their operations
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …

[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 networks for dimensionality reduction and large-scale optimization: Part 1 low-rank tensor decompositions

A Cichocki, N Lee, I Oseledets, AH Phan… - … and Trends® in …, 2016 - nowpublishers.com
Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods

AJA James, RM Konik, P Lecheminant… - Reports on Progress …, 2018 - iopscience.iop.org
We review two important non-perturbative approaches for extracting the physics of low-
dimensional strongly correlated quantum systems. Firstly, we start by providing a …

Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy)

J Hauschild, F Pollmann - SciPost Physics Lecture Notes, 2018 - scipost.org
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 …

Variational benchmarks for quantum many-body problems

D Wu, R Rossi, F Vicentini, N Astrakhantsev, F Becca… - Science, 2024 - science.org
The continued development of computational approaches to many-body ground-state
problems in physics and chemistry calls for a consistent way to assess its overall progress …

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 …

Coexistence of superconductivity with partially filled stripes in the Hubbard model

H Xu, CM Chung, M Qin, U Schollwöck, SR White… - Science, 2024 - science.org
The Hubbard model is an iconic model in quantum many-body physics and has been
intensely studied, especially since the discovery of high-temperature cuprate …

Variational optimization algorithms for uniform matrix product states

V Zauner-Stauber, L Vanderstraeten, MT Fishman… - Physical Review B, 2018 - APS
We combine the density matrix renormalization group (DMRG) with matrix product state
tangent space concepts to construct a variational algorithm for finding ground states of one …

Absence of superconductivity in the pure two-dimensional Hubbard model

M Qin, CM Chung, H Shi, E Vitali, C Hubig… - Physical Review X, 2020 - APS
We study the superconducting pairing correlations in the ground state of the doped Hubbard
model—in its original form without hop** beyond nearest neighbor or other perturbing …