Refining ensemble $N$-representability of one-body density matrices from partial information

Abstract

The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy of ensemble one-body $N$-representability problems that incorporate partial knowledge of the one-body reduced density matrices (1RDMs) within an ensemble of $N$-fermion states with fixed weights $w_i$. Specifically, we propose a systematic relaxation that reduces the refined problem -- where full 1RDMs are fixed for certain ensemble elements -- to a more tractable form involving only natural occupation number vectors. Remarkably, we show that this relaxed problem is related to a generalization of Horn's problem, enabling an explicit solution by combining its constraints with those of the weighted ensemble $N$-representability conditions. An additional convex relaxation yields a convex polytope that provides physically meaningful restrictions on lattice site occupations in ensemble density functional theory for excited states.

References in corpus (72)

• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Hartree-Fock on a superconducting qubit quantum computer
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• Quantum marginal problem and N-representability
• N-representability is QMA-complete
• Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
• Fermionic partial tomography via classical shadows
• The Pauli principle revisited
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Incompatible measurements in quantum information science
• Pinning of Fermionic Occupation Numbers
• Direct extraction of excitation energies from ensemble density-functional theory
• Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation
• Quantum state tomography via reduced density matrices
• Non-equilibrium Steady State Conductivity in Cyclo[18]carbon and Its Boron Nitride Analogue
• Relating the pure and ensemble density matrix functional
• Individual correlations in ensemble density-functional theory: State-driven/density-driven decompositions without additional Kohn-Sham systems
• Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• Gaussian quantum marginal problem
• Convexity of momentum map, Morse index, and quantum entanglement
• Quasipinning and its relevance for $N$-Fermion quantum states
• DoNOF: an open-source implementation of natural-orbital-functional-based methods for quantum chemistry
• Foundation of one-particle reduced density matrix functional theory for excited states
• Eigenvalue Distributions of Reduced Density Matrices
• A weight-dependent local correlation density-functional approximation for ensembles
• Quantum Many-body Theory from a Solution of the $N$-representability Problem
• A complete hierarchy for the pure state marginal problem in quantum mechanics
• Natural orbital functional for multiplets
• Reduced density-matrix functionals applied to the Hubbard dimer
• Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation
• Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials
• Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability
• Reconstructing quantum states from single-party information
• Refining and relating fundamentals of functional theory
• Electronic excited states in extreme limits via ensemble density functionals
• Generalized Pauli constraints in small atoms
• Quantum marginal problem and incompatibility
• Reduced Density Matrix Functional Theory for Superconductors
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Dual-Cone Variational Calculation of the 2-Electron Reduced Density Matrix
• Almost all four-particle pure states are determined by their two-body marginals
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Lattice density-functional theory on graphene
• Lattice Density-Functional Theory for Quantum Chemistry
• Deriving density-matrix functionals for excited states
• Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths
• Efficient Two-Electron Ansatz for Benchmarking Quantum Chemistry on a Quantum Computer
• Exploiting the hessian for a better convergence of the SCF RDMFT procedure
• Ground and Excited States from Ensemble Variational Principles
• Membership in moment polytopes is in NP and coNP
• Reducing the Quantum Many-electron Problem to Two Electrons with Machine Learning
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• Predicting The One-Particle Density Matrix With Machine Learning
• Static correlated functionals for reduced density matrix functional theory
• Ensemble density functional theory of ground and excited energy levels
• Data-driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory
• Quantum marginals from pure doubly excited states
• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• Beginnings of Exciton Condensation in Coronene Analog of Graphene Double Layer
• Recoupling coefficients and quantum entropies
• One-body reduced density-matrix functional theory for the canonical ensemble
• Geometry of Degeneracy in Potential and Density Space
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Adaptive cluster approximation for reduced density-matrix functional theory
• Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems
• Quantum tomography of Rydberg atom graphs by configurable ancillas
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain