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

Physics Letters A

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Antonios Gonis

Published Sep 2, 2016• 8 citations
Publisher
DOI
10.1016/j.physleta.2016.08.041

Related papers

Lack of Hohenberg-Kohn theorem for excited states in DFT and its consequences.

R. Gaudoin, Kieron Burke

APS•Mar 1, 2004•0 citations

Demonstration of the Gunnarsson-Lundqvist theorem and Lack of Hohenberg-Kohn Theorem for Excited States

Xiao‐Yin Pan, Yuqi Li, Biao Li +1 more

Bulletin of the American Physical Society•Mar 1, 2012•0 citations

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

Louis Garrigue

arXiv:1906.03191•Journal of Statistical Physics•Sep 10, 2019•16 citations

An exact one-particle theory of bosonic excitations: from a generalized Hohenberg–Kohn theorem to convexified N-representability

Julia Liebert, Christian Schilling

Abstract Motivated by the Penrose–Onsager criterion for Bose–Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an extension of the Rayleigh–Ritz variational principle to ensemble states with spectrum w and prove a corresponding generalization of the Hohenberg–Kohn theorem: the underlying one-particle reduced density matrix determines all properties of systems of N identical particles in their w -ensemble states. Then, to circumvent the v-representability problem common to functional theories, and to deal with energetic degeneracies, we resort to the Levy–Lieb constrained search formalism in combination with an exact convex relaxation. The corresponding bosonic one-body w -ensemble N-representability problem is solved comprehensively. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli’s exclusion principle for fermions and recently discovered generalizations thereof.

arXiv:2204.12715•New Journal of Physics•Jan 1, 2023•18 citations

Variational Principle for Many-Fermion Systems

Élliott H. Lieb

Physical Review Letters•Jul 6, 1981•33 citations

Nonexistence of a Hohenberg-Kohn variational principle in total current-density-functional theory

Andre Laestadius, Michael Benedicks

For a many-electron system, whether the particle density $\ensuremath{\rho}(\mathbf{r})$ and the total current density $\mathbf{j}(\mathbf{r})$ are sufficent to determine the one-body potential $V(\mathbf{r})$ and vector potential $A(\mathbf{r})$ is still an open question. For the one-electron case, a Hohenberg-Kohn theorem exists formulated with the total current density. Here we show that the generalized Hohenberg-Kohn energy functional ${\mathcal{E}}_{{V}_{0},{\mathbf{A}}_{0}}(\ensuremath{\rho},\mathbf{j})=\ensuremath{\langle}\ensuremath{\psi}(\ensuremath{\rho},\mathbf{j}),H({V}_{0},{\mathbf{A}}_{0})\ensuremath{\psi}(\ensuremath{\rho},\mathbf{j})\ensuremath{\rangle}$ can be minimal for densities that are not the ground-state densities of the fixed potentials ${V}_{0}$ and ${\mathbf{A}}_{0}$. Furthermore, for an arbitrary number of electrons and under the assumption that a Hohenberg-Kohn theorem exists formulated with $\ensuremath{\rho}$ and $\mathbf{j}$, we discuss the possibility of a variational principle in total current-density-functional theory such as that of Hohenberg-Kohn.

arXiv:1404.3297•Physical Review A•Mar 23, 2015•18 citations
Abstract Motivated by the Penrose–Onsager criterion for Bose–Einstein condensation we propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. For this, we employ an extension of the Rayleigh–Ritz variational principle to ensemble states with spectrum w and prove a corresponding generalization of the Hohenberg–Kohn theorem: the underlying one-particle reduced density matrix determines all properties of systems of N identical particles in their w -ensemble states. Then, to circumvent the v-representability problem common to functional theories, and to deal with energetic degeneracies, we resort to the Levy–Lieb constrained search formalism in combination with an exact convex relaxation. The corresponding bosonic one-body w -ensemble N-representability problem is solved comprehensively. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli’s exclusion principle for fermions and recently discovered generalizations thereof.
For a many-electron system, whether the particle density $\ensuremath{\rho}(\mathbf{r})$ and the total current density j(r)\mathbf{j}(\mathbf{r})j(r) are sufficent to determine the one-body potential V(r)V(\mathbf{r})V(r) and vector potential A(r)A(\mathbf{r})A(r) is still an open question. For the one-electron case, a Hohenberg-Kohn theorem exists formulated with the total current density. Here we show that the generalized Hohenberg-Kohn energy functional ${\mathcal{E}}_{{V}_{0},{\mathbf{A}}_{0}}(\ensuremath{\rho},\mathbf{j})=\ensuremath{\langle}\ensuremath{\psi}(\ensuremath{\rho},\mathbf{j}),H({V}_{0},{\mathbf{A}}_{0})\ensuremath{\psi}(\ensuremath{\rho},\mathbf{j})\ensuremath{\rangle}$ can be minimal for densities that are not the ground-state densities of the fixed potentials V0{V}_{0}V0​ and A0{\mathbf{A}}_{0}A0​. Furthermore, for an arbitrary number of electrons and under the assumption that a Hohenberg-Kohn theorem exists formulated with $\ensuremath{\rho}$ and j\mathbf{j}j, we discuss the possibility of a variational principle in total current-density-functional theory such as that of Hohenberg-Kohn.