Multiple impurities and combined local density approximations in site-occupation embedding theory

Abstract

Site-occupation embedding theory (SOET) is an in-principle-exact multi-determinantal extension of density-functional theory for model Hamiltonians. Various extensions of recent developments in SOET [Senjean et al., Phys. Rev. B 97, 235105 (2018)] are explored in this work. An important step forward is the generalization of the theory to multiple impurity sites. We also propose a new single-impurity density-functional approximation (DFA) where the density-functional impurity correlation energy of the two-level (2L) Hubbard system is combined with the Bethe ansatz local density approximation (BALDA) to the full correlation energy of the (infinite) Hubbard model. In order to test the new DFAs, the impurity-interacting wavefunction has been computed selfconsistently with the density matrix renormalization group method (DMRG). Double occupation and per-site energy expressions have been derived and implemented in the one-dimensional case. A detailed analysis of the results is presented, with a particular focus on the errors induced either by the energy functionals solely or by the self-consistently converged densities. Among all the DFAs (including those previously proposed), the combined 2L-BALDA is the one that performs the best in all correlation and density regimes. Finally, extensions in new directions, like a partition-DFTtype reformulation of SOET, a projection-based SOET approach, or the combination of SOET with Green functions, are briefly discussed as a perspective. arXiv:1806.06057v2 [cond-mat.str-el]

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

“…Unlike in the exact theory, the 2L approximate impurity-interacting correlation potential does not exhibit a derivative discontinuity at n 0 = 1 for finite U/t values. This is due to the fact that the twoelectron Anderson dimer it originates from is a closed system [55,57]. One could make the same comment about the 2L impurity-interacting density-functional selfenergy.…”

“…More details can be found in Refs. [56,57]. We start from the (grand canonical) 1D Hubbard Hamiltonian,Ĥ…”

“…Various local density-functional approximations to the impurity correlation energy have been explored in Refs. [56] and [57]. In this work, we will use the one extracted from the two-level (2L) Anderson model [55] which can be expressed as follows:…”

“…The formulas to calculate the exact impurity potential ∆v imp Hxc (U, n 0 ) for the asymmetric Hubbard dimer have been derived in Refs. [57,63,64]. In the symmetric Anderson dimer (v 0 = −U/2, v 1 = 0) and n = 1, there is an analytic expression for the exact impurity Green's function and self-energy [66],…”

“…Note also that the use of other (frequency-independent) reduced quantities, such as the one-body density matrix, has been considered in the so-called lattice DFT [47][48][49][50][51][52][53]. In recent years, an in-principle-exact alternative formulation of SOFT, referred to as site-occupation embedding theory (SOET) [54][55][56][57], has been explored. In contrast to standard Kohn-Sham (KS) DFT, SOET maps the whole physical system onto an impurity-interacting one.…”