Abstract
Quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected "impurity+bath" cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the (Householder transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are not described neither in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.
Highlights
Quantum embedding has emerged over the last two decades as a viable strategy for modelling strong electron correlation in large molecules and extended systems [1]
We describe in detail the embedding of a single impurity in the one-dimensional (1D) Hubbard model
In the simplest embedding scheme, which is described in the present work, electron correlation is introduced within the cluster while freezing the Householder vector to its NI value
Summary
Quantum embedding has emerged over the last two decades as a viable strategy for modelling strong electron correlation in large molecules and extended systems [1]. In the well-established dynamical mean-field theory (DMFT) [2,3,4,5,6], the so-called local Green function, which is evaluated on the impurity, is the quantity of interest In this case, the non-interacting sites of the Anderson model (on which the Green function is mapped) represent the bath. This is achieved via a unitary Householder transformation [53] In this approach, that we refer to as Householder transformed density-matrix functional embedding theory (Ht-DMFET), the bath orbital becomes a simple and analytical functional of the (possibly correlated) density matrix, greatly simplifying its construction, even in the commonly used non-interacting (or mean-field) case.
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