Tensor networks for dimensionality reduction and large-scale optimization: Part 2 applications and future perspectives
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 …
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …
[HTML][HTML] Time-evolution methods for matrix-product states
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 …
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
Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …
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
We review two important non-perturbative approaches for extracting the physics of low-
dimensional strongly correlated quantum systems. Firstly, we start by providing a …
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 …
many-body systems in and out of equilibrium. In particular, the one-dimensional matrix …
Variational benchmarks for quantum many-body problems
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 …
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
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 …
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
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 …
intensely studied, especially since the discovery of high-temperature cuprate …
Variational optimization algorithms for uniform matrix product states
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 …
tangent space concepts to construct a variational algorithm for finding ground states of one …
Absence of superconductivity in the pure two-dimensional Hubbard model
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 …
model—in its original form without hop** beyond nearest neighbor or other perturbing …