Householder transformed density matrix functional embedding theory

TL;DR

This paper introduces a new quantum embedding method based on the Householder transformation that accurately captures electron correlation effects in lattice models, improving upon existing density matrix embedding techniques.

Contribution

The paper presents Householder transformed density matrix functional embedding theory (Ht-DMFET), a novel approach that preserves the single-particle character and simplifies the embedding process compared to traditional methods.

Findings

Per-site energies match Bethe Ansatz results in half-filled 1D Hubbard model.

Results deteriorate away from half-filling due to electron number fluctuations.

Increasing the number of impurities improves energy accuracy.

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.