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

Abstract

A reformulation of site-occupation embedding theory (SOET) in terms of Green's functions is presented. Referred to as site-occupation-Green's function embedding theory (SOGET), this novel extension of density-functional theory for model Hamiltonians shares many features with dynamical mean-field theory (DMFT) but is formally exact (in any dimension). In SOGET, the impurity-interacting correlation potential becomes a density-functional self-energy which is frequency-dependent and in principle non-local. A simple local density-functional approximation (LDA) combining the Bethe Ansatz (BA) LDA with the self-energy of the two-level Anderson model is constructed and successfully applied to the one-dimensional Hubbard model. Unlike in previous implementations of SOET, no many-body wavefunction is needed, thus reducing drastically the computational cost of the method.

Exchange-correlation potentials for multi-orbital quantum dots subject to generic density-density interactions and Hund's rule coupling

“…4). We start with the CIM potential and show that an excellent parametrization of the Hxc potential can be achieved by simply summing the (exact) SSM potential (22) over the charging states of the dot, and shifting and rescaling it such that the potential does not become negative or larger than (2M − 1)U :…”

“…However, this approach is hampered by the so-called doublecounting problem 19 , limiting its predictivity. More recently, however, new efforts in combining DFT with lattice models avoiding the double-counting problem [20][21][22] or to solve the double-counting problem in DFT+DMFT 23 have been undertaken.…”

A Versatile Unitary Transformation Framework for an Optimal Bath Construction in Density-Matrix Based Quantum Embedding Approaches

“…In particular, within the dynamical mean-field theory (DMFT) formal-ism [8][9][10], the effective Hamiltonian is an effective Anderson impurity model (AIM) [11], and is derived self-consistently using the Green's function of the system. Note that various alternative embedding approaches using the Green's function have been developed to derive effective AIM [12][13][14] or other effective Hamiltonians [15,16].…”

Quantum embedding for material chemistry based on domain separation and open subsystems

“…Nowadays there is a wide set of quantum embedding theories/methods that are being developed, and some of them are already used in practical calculations. Just to name a few: subsystem DFT, 1–4 frozen density embedding, 5–8 dynamical mean‐field theory, 9–11 Green's function embedding, 12–13 density matrix embedding, 14–17 site‐occupation embedding 18–23 (recently this theory has been combined with density matrix embedding, ref. 24 ), partition DFT, 25–28 projection‐based embedding, 29–31 potential‐functional embedding, 32–34 and WFT‐in‐WFT embedding 35–36 .…”

“…embedding, [12,13] density matrix embedding, [14][15][16][17] site-occupation embedding [18][19][20][21][22][23] (recently this theory has been combined with density matrix embedding, ref. [24]), partition DFT, [25][26][27][28] projection-based embedding, [29][30][31] potential-functional embedding, [32][33][34] and WFT-in-WFT embedding.…”