Generalized Pauli constraints in reduced density matrix functional theory

Abstract

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman's ensemble $N$-representability conditions. Recently, the topic of pure-state $N$-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble $N$-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.

References in corpus (16)

• A natural orbital functional for the many-electron problem
• Quantum marginal problem and N-representability
• Reduced Density Matrix Functional for Many-Electron Systems
• The Pauli principle revisited
• Pinning of Fermionic Occupation Numbers
• Density-Matrix-Power Functional: Performance for Finite Systems and the Homogeneous Electron Gas
• Empirical Functionals for Reduced Density Matrix Functional Theory
• Spectral density and metal-insulator phase transition in Mott insulators within RDMFT
• Benchmark calculations for reduced density-matrix functional theory
• Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules
• Quasi-pinning and entanglement in the lithium isoelectronic series
• Open shells in reduced-density-matrix-functional theory
• Quasipinning and its relevance for $N$-Fermion quantum states
• Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6
• Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
• Quasi-particle energy spectra in local reduced density matrix functional theory

Cited by in corpus (30)

• Towards a formal definition of static and dynamic electronic correlations
• Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition
• Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
• Reduced Density-Matrix Approach to Strong Matter-Photon Interaction
• Foundation of one-particle reduced density matrix functional theory for excited states
• Phase Dilemma in Natural Orbital Functional Theory from the N-representability Perspective
• Quasipinning and selection rules for excitations in atoms and molecules
• Hubbard model: Pinning of occupation numbers and role of symmetries
• Reconstructing quantum states from single-party information
• Generalized Pauli constraints in small atoms
• Pinning of Fermionic Occupation Numbers: General Concepts and One Dimension
• Experimental Data from a Quantum Computer Verifies the Generalized Pauli Exclusion Principle
• Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom
• Exploiting the hessian for a better convergence of the SCF RDMFT procedure
• Role of the pair potential for the saturation of generalized Pauli constraints
• Static correlated functionals for reduced density matrix functional theory
• On the time evolution of fermionic occupation numbers
• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• High ground state overlap via quantum embedding methods
• Kinetic-Energy Density-Functional Theory on a Lattice
• Potential energy curve for the $a^3{\Sigma }_u^{+}$ state of lithium dimer with Slater-type orbitals
• Conditions for describing triplet states in reduced density matrix functional theory
• Natural orbital functional for spin-polarized periodic systems
• Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain
• Determining the N-representability of a reduced density matrix via unitary evolution and stochastic sampling
• Structure of the first order Reduced Density Matrix in three electron systems: A Generalized Pauli Constraints assisted study
• Impact of Parametrizations of the One-Body Reduced Density Matrix on the Energy Landscape
• Determining the ensemble N-representability of Reduced Density Matrices