Local Potential Functional Embedding Theory of Molecular Systems: Localized Orbital-Based Embedding from an Exact Density-Functional Perspective

Abstract

Localized orbital-based quantum embedding, as originally formulated in the context of density matrix embedding theory (DMET), is revisited from the perspective of lattice density functional theory (DFT). An in-principle exact (in the sense of full configuration interaction) formulation of the theory, where the occupations of the localized orbitals play the role of the density, is derived for any (model or ab initio) electronic Hamiltonian. From this general formalism we deduce an exact relation between the local Hartree-exchange-correlation (Hxc) potential of the full-size Kohn-Sham (KS) lattice-like system and the embedding chemical potential that is adjusted on each embedded fragment, individually, such that both KS and embedding cluster systems reproduce the exact same local density. When well-identified density-functional approximations (that find their justification in the strongly correlated regime) are applied, a practical self-consistent local potential functional embedding theory (LPFET), where the local Hxc potential becomes the basic variable, naturally emerges from the theory. LPFET differs from previous density embedding approaches by its fragment-dependent embedding chemical potential expression, which is a simple functional of the Hxc potential. Numerical calculations on prototypical systems show the ability of such an ansatz to improve substantially the description of density profiles (localized orbitals occupation numbers in this context) in strongly correlated systems.

References in corpus (71)

• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Density matrix embedding: A strong-coupling quantum embedding theory
• Quantum embedding theories
• A practical guide to density matrix embedding theory in quantum chemistry
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• Quantum simulations of materials on near-term quantum computers
• Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
• Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory
• Dynamical mean-field theory from a quantum chemical perspective
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• Exactly-embedded multiconfigurational self-consistent field theory using density matrix embedding: the localized active space self-consistent field method
• Electron correlation in solids via density embedding theory
• What can Mott insulators teach us about density-functional theory (and vice versa)?
• Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
• Systematic electronic structure in the cuprate parent state from quantum many-body simulations
• The Variational Localized Active Space Self-Consistent Field Method
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Generalized self-energy embedding theory
• Spectral functions of strongly correlated extended systems via an exact quantum embedding
• Systematic improvability in quantum embedding for real materials
• Rigorous wave function embedding with dynamical fluctuations
• On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation
• Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
• Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver
• Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model
• Cluster Density Matrix Embedding Theory for Quantum Spin Systems
• Energy-weighted density matrix embedding of open correlated chemical fragments
• Local density approximation in site-occupation embedding theory
• Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model
• Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding
• Fully Algebraic and Self-consistent Effective Dynamics in a Static Quantum Embedding
• Density matrix embedding theory for interacting electron-phonon systems
• Five years of density matrix embedding theory
• Embedding via the Exact Factorization Approach
• Projected Density Matrix Embedding Theory with Applications to the Two-Dimensional Hubbard Model
• Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations
• Block product density matrix embedding theory for strongly correlated spin systems
• Householder transformed density matrix functional embedding theory
• Rigorous screened interactions for realistic correlated electron systems
• On the effective reconstruction of expectation values from ab initio quantum embedding
• Incremental Embedding: A Density Matrix Embedding Scheme for Molecules
• Extending Density Matrix Embedding: A Static Two-Particle Theory
• Ab initio quantum many-body description of superconducting trends in the cuprates
• Dealing with the exponential wall in electronic structure calculations
• Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting
• Fock space embedding theory for strongly correlated topological phases
• Multiscale Embedding for Quantum Computing
• Projected site-occupation embedding theory
• Uniqueness of density-to-potential mapping for fermionic lattice systems
• Multi-site Reaction Dynamics Through Multi-fragment Density Matrix Embedding
• Interacting-bath dynamical embedding for capturing non-local electron correlation in solids
• Quantum embedding of multi-orbital fragments using the Block-Householder-transformation
• High ground state overlap via quantum embedding methods
• Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals
• A unified density-matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation
• Derivation of the Ghost Gutzwiller Approximation from Quantum Embedding principles: the Ghost Density Matrix Embedding Theory
• Testing density-functional approximations on a lattice and the limits of the related Hohenberg-Kohn-type theorem
• Quantum embedding for molecules using auxiliary particles -- The ghost Gutzwiller Ansatz
• Geometry of Degeneracy in Potential and Density Space
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Entanglement spectrum as a marker for phase transitions in the density embedding theory for interacting spinless fermionic models
• Multiple impurities and combined local density approximations in Site-Occupation Embedding Theory
• Comparative study of the density matrix embedding theory for the Hubbard models
• Simple embedding scheme for the spectral properties of the Single-Impurity Anderson Model
• FragPT2: Multi-Fragment Wavefunction Embedding with Perturbative Interactions
• Fragment quantum embedding using the Householder transformation: a multi-state extension based on ensembles
• Unitary transformations within density matrix embedding approaches: A novel perspective on the self-consistent scheme for electronic structure calculation

Cited by in corpus (2)

• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
• Ghost Embedding Bridging Chemistry and One-Body Theories