scholarly journals Insights into one-body density matrices using deep learning

2020 ◽  
Vol 224 ◽  
pp. 265-291 ◽  
Author(s):  
Jack Wetherell ◽  
Andrea Costamagna ◽  
Matteo Gatti ◽  
Lucia Reining
Keyword(s):  
Deep Learning ◽  
Density Matrix ◽  
Reduced Density Matrix ◽  
Body Density ◽  
Density Matrices ◽  
Learning Constraints ◽  
The One ◽  
Reduced Density

Deep-learning constraints of the one-body reduced density matrix from its compressibility to enable efficient determination of key observables.

Time dependent reduced density matrix functional theory at strong correlation: insights from a two-site Anderson impurity model

2021 ◽  
Author(s):  
Stefano Di Sabatino ◽  
Claudio Verdozzi ◽  
Pina Romaniello
Keyword(s):  
Density Matrix ◽  
Strong Correlation ◽  
Time Dependent ◽  
Reduced Density Matrix ◽  
Body Density ◽  
Functional Theory ◽  
Impurity Model ◽  
Anderson Impurity Model ◽  
The One ◽  
Reduced Density

The one-body density matrix has recently attracted considerable attention as promising key quantity for the description of systems out of equilibrium. Its time evolution is given in terms of the...

scholarly journals Unrestricted treatment for the direct variational determination of the two-electron reduced density matrix for doubly occupied-configuration-interaction wave functions

2019 ◽  
Vol 150 (16) ◽  
pp. 164106 ◽  
Author(s):  
Diego R. Alcoba ◽  
Alicia Torre ◽  
Luis Lain ◽  
Gustavo E. Massaccesi ◽  
Ofelia B. Oña ◽  
...  
Keyword(s):  
Density Matrix ◽  
Configuration Interaction ◽  
Wave Functions ◽  
Reduced Density Matrix ◽  
Reduced Density

Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions

2006 ◽  
Vol 125 (24) ◽  
pp. 244109 ◽  
Author(s):  
Maho Nakata ◽  
Bastiaan J. Braams ◽  
Mituhiro Fukuda ◽  
Jerome K. Percus ◽  
Makoto Yamashita ◽  
...  
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Reduced Density

scholarly journals Entropic entanglement criteria for fermion systems

2013 ◽  
Vol 32 (1) ◽  
Author(s):  
Claudia Zander
Keyword(s):  
Density Matrix ◽  
Reduced Density Matrix ◽  
Total System ◽  
Mixed States ◽  
Fermion Systems ◽  
The One ◽  
Reduced Density ◽  
Global Density

Entanglement criteria for general (pure or mixed) states of systems consisting of N identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system and the entropy of the one-particle, reduced density matrix.

scholarly journals Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

2020 ◽  
Author(s):  
Jonathon Misiewicz ◽  
Justin Turney ◽  
Henry Schaefer
Keyword(s):  
Density Matrix ◽  
Generating Function ◽  
Reduced Density Matrix ◽  
General Mechanism ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Normal Ordering ◽  
Combinatorial Constructions ◽  
Reduced Density

Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering, but the underlying formalism has remained mysterious. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical to equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and reduced density matrices are entirely combinatorial constructions, where the differences can be associated to changes in the notion of "multiplicative separability'' for expectation values of random variables compared to reduced density matrices. We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present the simplest proof to date of the Generalized Normal Ordering formalism to explore the role of reduced density matrix cumulants therein.

On the Inference of the One-Particle Density Matrix from Position and Momentum-Space Form Factors

1993 ◽  
Vol 48 (1-2) ◽  
pp. 211-220
Author(s):  
Hartmut Schmider ◽  
Vedene H. Smith, Jr. ◽  
Wolf Weyrich
Keyword(s):  
Density Matrix ◽  
Electron Correlation ◽  
Momentum Space ◽  
Space Form ◽  
Particle Density ◽  
Form Factors ◽  
Reduced Density Matrix ◽  
Expectation Values ◽  
The One ◽  
Reduced Density

Abstract A modification of a recently developed method for the least-squares reconstruction of a one-particle reduced density matrix from experimentally accessible expectation values is applied to the test systems of atomic beryllium and neon. The improvement of the resulting matrices through inclusion of electron correlation is demonstrated. Their quality is judged by comparison of the moments of the position and momentum densities and of the spherically averaged density matrix in a suitable representation.

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