# Orthogonalization of fermion k -body operators and representability

@article{Bach2018OrthogonalizationOF, title={Orthogonalization of fermion k -body operators and representability}, author={Volker Bach and Robert Rauch}, journal={Physical Review A}, year={2018} }

The reduced k-particle density matrix of a density matrix on finite-dimensional, fermion Fock space can be defined as the image under the orthogonal projection in the Hilbert-Schmidt geometry onto the space of k-body observables. A proper understanding of this projection is therefore intimately related to the representability problem, a long-standing open problem in computational quantum chemistry. Given an orthonormal basis in the finite-dimensional one-particle Hilbert space, we explicitly…

## One Citation

### An Effective Solution to Convex 1-Body N-Representability

- MathematicsAnnales Henri Poincaré
- 2023

From a geometric point of view, Pauli's exclusion principle defines a hypersimplex. This convex polytope describes the compatibility of $1$-fermion and $N$-fermion density matrices, therefore it…

## References

SHOWING 1-10 OF 20 REFERENCES

### Quasiparticle Fock-space coupled-cluster theory

- Physics
- 2010

The quasiparticle Fock-space coupled-cluster (QFSCC) theory, introduced by us in 1985, is described. This is a theory of many-electron systems which uses the second-quantisation formalism based on…

### Current-constrained density-matrix theory to calculate molecular conductivity with increased accuracy

- PhysicsCommunications Chemistry
- 2018

Molecular conductivity is the quantum flow of electrons through a molecule. Since its conception by Aviram and Ratner, molecular conductivity has been realized experimentally in molecules and…

### THE STRUCTURE OF FERMION DENSITY MATRICES

- Physics
- 1963

Abstract : A new approach is presented to the many-particle problem in quantum mechanics by proposing a method of finding natural orbitals and natural geminals of a system without prior knowledge of…

### Reduction of the N‐Particle Variational Problem

- Physics
- 1964

A variational method is presented which is applicable to N‐particle boson or fermion systems with two‐body interactions. For these systems the energy may be expressed in terms of the two‐particle…

### Reduced Density Matrices: Coulson's Challenge

- Physics
- 2000

1 Basic properties.- 1.1 Reduced Density Matrices.- 1.2 N-representability.- 1.3 Norbs, Nags and Least Squares.- 1.4 Fock Space.- 1.5 Reduced Density Matrices on Fock Space.- 1.6 Unitary Invariance.-…

### Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors

- Physics
- 1962

This review is concerned with the concept that in a many-body system of bosons or fermions, it is possible to have an off-diagonai long-range order of the reduced density matrices in the coordinate…

### Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules

- Biology
- 2007

This work focuses on the development of a single theory, called the two-ELECTRON REDUCED-DENSITY-MATRIX Theory, which aims to explain the phenomenon of dual-use electronics and its applications in the context of energy efficiency and social justice.