Site-Occupation Embedding Theory using Bethe Ansatz Local Density Approximations

Abstract

Site-occupation embedding theory (SOET) is an alternative formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a non-interacting) one. It provides a rigorous framework for combining wavefunction (or Green function) based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wavefunction has been performed with the density matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Regular article with 14 pages including 6 figures

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum embedding theories
• Multitier self-consistent $GW$+EDMFT
• Systematically improvable multi-scale solver for correlated electron systems
• Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas
• On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation
• Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
• Testing self-energy embedding theory in combination with GW
• Solving lattice density functionals close to the Mott regime
• Effects of disorder on atomic density waves and spin-singlet dimers in one-dimensional optical lattices

Cited by in corpus (16)

• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions
• Householder transformed density matrix functional embedding theory
• Quantum System Partitioning at the Single-Particle Level
• Lattice Density-Functional Theory for Quantum Chemistry
• Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths
• Fock space embedding theory for strongly correlated topological phases
• Projected site-occupation embedding theory
• Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals
• Multiple impurities and combined local density approximations in Site-Occupation Embedding Theory
• Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain
• Unitary transformations within density matrix embedding approaches: A novel perspective on the self-consistent scheme for electronic structure calculation
• Site-occupation--Green's function embedding theory: A density-functional approach to dynamical impurity solvers
• On the pure state $v$-representability of density matrix embedding theory
• Local Potential Functional Embedding Theory of Molecular Systems: Localized Orbital-Based Embedding from an Exact Density-Functional Perspective
• Efficient slave-boson approach for multiorbital two-particle response functions and superconductivity