Sum-over-poles framework for quantum embedding to approach the real-frequency axis
Abstract
We introduce a real-frequency framework for the quantum embedding of solids, based on sum-over-poles (SOP) representations. We partition the lattice into periodically repeated interacting fragments and derive an embedded Dyson equation for the fragment, to be solved self-consistently. The resulting scheme generalizes the algorithmic-inversion method of our previous work to interacting Hamiltonians and is closely related to dynamical mean-field theory (DMFT), especially when an extended impurity problem is introduced. By exploiting the compact pole expansion of the embedding potential, we carry out the self-consistent procedure close to the real axis, which avoids ill-posed analytic continuation. In addition, the SOP representation allows us to introduce a pole-and-residue dynamics, which we use to reach the self-consistent solution. After deriving the method, we benchmark it against exact-diagonalization implementations of DMFT on the one-dimensional Hubbard ring at half filling. The framework offers a natural route to real-space dynamical quantum embedding, for periodic systems as well as for strongly correlated defects in materials.
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BibTeX
@misc{carbone2026sumoverpoles,
title = {{Sum-over-poles framework for quantum embedding to approach the real-frequency axis}},
author = {Alessandro Carbone and Massimo Capone and Nicola Marzari and Tommaso Chiarotti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28472},
eprint = {2610.28472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28472},
}
RIS
TY - UNPB
TI - Sum-over-poles framework for quantum embedding to approach the real-frequency axis
AU - Alessandro Carbone
AU - Massimo Capone
AU - Nicola Marzari
AU - Tommaso Chiarotti
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28472
UR - https://arxiv.org/abs/2610.28472
AB - We introduce a real-frequency framework for the quantum embedding of solids, based on sum-over-poles (SOP) representations. We partition the lattice into periodically repeated interacting fragments and derive an embedded Dyson equation for the fragment, to be solved self-consistently. The resulting scheme generalizes the algorithmic-inversion method of our previous work to interacting Hamiltonians and is closely related to dynamical mean-field theory (DMFT), especially when an extended impurity problem is introduced. By exploiting the compact pole expansion of the embedding potential, we carry out the self-consistent procedure close to the real axis, which avoids ill-posed analytic continuation. In addition, the SOP representation allows us to introduce a pole-and-residue dynamics, which we use to reach the self-consistent solution. After deriving the method, we benchmark it against exact-diagonalization implementations of DMFT on the one-dimensional Hubbard ring at half filling. The framework offers a natural route to real-space dynamical quantum embedding, for periodic systems as well as for strongly correlated defects in materials.
ER -