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

Journal of Mathematical Physics

Particle-Hole Matrix: Its Connection with the Symmetries and Collective Features of the Ground State

Claude Garrod, Mitja Rosina

Published Oct 1, 1969• 81 citations
Publisher

Abstract

A detailed study is made of the properties of the ``particle-hole matrix''Gabcd≡〈g| (a†b−ρab)†(c†d−ρcd) |g〉,where |g> is a many-fermion ground state and ρab is the 1-body density matrix. It is shown that the zero eigenvalues of the particle-hole matrix are intimately and simply related to the one-body symmetries of the ground state. It is also shown that the large eigenvalues of Gabcd are closely related to the collective features of the ground state.

DOI
10.1063/1.1664770

Related papers

Ground-state properties of hard-core bosons in one-dimensional harmonic traps

T. Papenbrock

The one-particle density matrices for hard-core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground-state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard-core bosons is similar to that of noninteracting fermions.

arXiv:cond-mat/0209300•Physical Review A•Apr 10, 2003•72 citations

Density-matrix functional theory for the N-particle ground state

Gil Zumbach, Klaus Maschke

We discuss the one-particle density-matrix functional theory for the N-particle ground-state problem. Using the variational principle we obtain a set of self-consistent equations which could be useful for practical calculations. The derived relation between the eigenvalues of the density matrix and the chemical potential agrees with that of Gilbert. The present theory is compared with the Kohn–Sham and the Hartree–Fock approach to the ground state problem. It is found that both approaches can be obtained from the present theory under certain assumptions.

The Journal of Chemical Physics•Jun 15, 1985•72 citations

Collective particle hole excitation in a deformed ground state

W. D. Heiss, Richard H. Lemmer

It is shown that stable collective particle hole excitations are possible in a generalized Hartree-Fock basis which describes a ground state that has less symmetry than the Hamiltonian. It appears that these collective states remain stable also for strong attractive interaction.[NUCLEAR STRUCTURE Nuclear matter density fluctuations, generalized random phase approximation.]

Physical Review C•Jun 1, 1984•6 citations

Direct variational calculation of two-body density matrix and a calculation of particle--hole states determined by two-body density matrix of the ground state

Miodrag V. Mihailović, Judit Németh

•Jan 1, 1974•0 citations

A formula to calculate particle-hole excited states if the two-body density matrix of the ground state is known

Rosina, M., Mihailović, M. V.

•Jan 1, 1972•0 citations

A density functional perspective for single-particle systems

H. L. Neal

Density functional theory is discussed in the context of single-particle systems in one spatial dimension. We show that the ground state density ρ0(x) and energy E0 are simply related to a family of external potential energy functions with ground state wave functions ψn(x)∝ρ0(x)n and energies En=2nE0 for certain integer values of n.

arXiv:quant-ph/0306070•American Journal of Physics•Apr 13, 2004•2 citations
A detailed study is made of the properties of the ``particle-hole matrix''Gabcd≡〈g| (a†b−ρab)†(c†d−ρcd) |g〉,where |g> is a many-fermion ground state and ρab is the 1-body density matrix. It is shown that the zero eigenvalues of the particle-hole matrix are intimately and simply related to the one-body symmetries of the ground state. It is also shown that the large eigenvalues of Gabcd are closely related to the collective features of the ground state.
The one-particle density matrices for hard-core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground-state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard-core bosons is similar to that of noninteracting fermions.
We discuss the one-particle density-matrix functional theory for the N-particle ground-state problem. Using the variational principle we obtain a set of self-consistent equations which could be useful for practical calculations. The derived relation between the eigenvalues of the density matrix and the chemical potential agrees with that of Gilbert. The present theory is compared with the Kohn–Sham and the Hartree–Fock approach to the ground state problem. It is found that both approaches can be obtained from the present theory under certain assumptions.