Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer eBooks

Density Matrix and Statistical Tensors

Vsevolod V. Balashov, Alexei N. Grum-Grzhimailo, Nikolai M. Kabachnik

Published Jan 1, 2000• 1 citation
Publisher
DOI
10.1007/978-1-4757-3228-3_1

Related papers

Density Matrix and Statistical Tensors

Springer eBooks•Jan 1, 2002•0 citations

Characterization of the Density Matrix in Terms of Statistical Tensor Parameters

Sakineh Ashourisheikhi

It was shown in literatures that every density matrix for a spin-� system can be defined in terms of the Fano statistical tensor parameters. On the other hand, this spherical tensor parameters can be uniquely determined by units vectors. In this study, we construct the density matrix for the most general spin-1 system in terms of unit vectors. We also give some cases to show symmetric properties of spherical tensor parameters.

•Jan 1, 2014•0 citations

Density Matrices

Klaus Bartschat

Springer handbooks•Jan 1, 2023•0 citations

Vertical density matrix algorithm: A higher-dimensional numerical renormalization scheme based on the tensor product state ansatz

Nobuya Maeshima, Yasuhiro Hieida, Yasuhiro Akutsu +2 more

We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors that are iteratively optimized by the use of the "vertical density matrix" formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation, we can also apply the VDMA to 2D quantum systems, which we demonstrate for the 2D transverse field Ising model.

arXiv:cond-mat/0101360•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 26, 2001•73 citations

DENSITY MATRICES

Mitchel Weissbluth

Elsevier eBooks•Jan 1, 1978•1 citation

Tensor product expansions for correlation in quantum many-body systems

Gábor Cśanyi, T. A. Arias

We explore a class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of the one-body matrix. Representing dynamical correlation alone as a single tensor product results in a theory that predicts near zero dynamical correlation in the homogeneous electron gas at moderate to high densities. But, representing both dynamical and statistical correlation effects together as a tensor product leads to the recently proposed ``natural orbital functional.'' We find that this latter theory has some asymptotic properties consistent with established many-body theory but is no more accurate than Hartree-Fock in describing the homogeneous electron gas for the range of densities typically found in the valence regions of solids.

arXiv:cond-mat/9805388•Physical review. B, Condensed matter•Mar 15, 2000•133 citations
We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors that are iteratively optimized by the use of the "vertical density matrix" formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation, we can also apply the VDMA to 2D quantum systems, which we demonstrate for the 2D transverse field Ising model.
We explore a class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of the one-body matrix. Representing dynamical correlation alone as a single tensor product results in a theory that predicts near zero dynamical correlation in the homogeneous electron gas at moderate to high densities. But, representing both dynamical and statistical correlation effects together as a tensor product leads to the recently proposed ``natural orbital functional.'' We find that this latter theory has some asymptotic properties consistent with established many-body theory but is no more accurate than Hartree-Fock in describing the homogeneous electron gas for the range of densities typically found in the valence regions of solids.