Compact representation of strongly correlated Green's functions: the MOR+EC way to explore phase space
Abstract
Repeated evaluation of the single-particle Green's function (GF) across parameter space is a recurring bottleneck in many-body methods, limiting the resolution at which phase boundaries may be probed and the frequency resolution of computed spectra. We introduce MOR+EC, a framework that constructs reusable reduced-order models for computing single-particle Green's functions by combining eigenvector continuation (EC) for parameter space exploration and model order reduction (MOR) for extrapolation in frequency space. Contrary to conventional parameterized MOR, we construct these reduced-order models with a parameter-independent resolvent, further reducing the number of required full-space evaluations. Benchmarking against exact diagonalization as the impurity solver for our example case of DMFT calculations for single- and two-band models, MOR+EC reproduces the DMFT-converged impurity GF to an average relative error below 10−3, with a median wall-time speedup of $9.5−92\times$. This accuracy and efficiency together resolve a fine-grained scan of the impurity occupation as doping is tuned and produce a high-resolution phase diagram of an orbital-selective Mott transition. The reduced-order model also reproduces real- and imaginary-frequency spectra at no additional cost in full-space evaluations. This framework applies broadly to GF-based methods requiring repeated parametric evaluation and high resolution of the frequency axis.
Related
- Compact and stable representation of real-frequency spectral functions for machine learning
- Pauli propagation enables fast classical simulation of strongly correlated quantum systems
- Ground-State Properties of a Lattice-Coupled Strongly Correlated Model for Solid Oxygen under Pressure
- Automated Symbolic Derivation Enables Scalable Ensemble DFT for Strongly Correlated Molecules and Materials
- Prominent Dimensional Effects on High-order Harmonic Generation in Strongly Correlated Electron Systems
BibTeX
@misc{hogan2026compact,
title = {{Compact representation of strongly correlated Green's functions: the MOR+EC way to explore phase space}},
author = {Norman Hogan and A. Kemper and Carlos Mejuto-Zaera},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28647},
eprint = {2609.28647},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05840353v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Compact representation of strongly correlated Green's functions: the MOR+EC way to explore phase space
AU - Norman Hogan
AU - A. Kemper
AU - Carlos Mejuto-Zaera
PY - 2026
DA - 2026/10/21
PB - HAL
DO - 10.48550/arxiv.2609.28647
UR - https://hal.science/hal-05840353v1
AB - Repeated evaluation of the single-particle Green's function (GF) across parameter space is a recurring bottleneck in many-body methods, limiting the resolution at which phase boundaries may be probed and the frequency resolution of computed spectra. We introduce MOR+EC, a framework that constructs reusable reduced-order models for computing single-particle Green's functions by combining eigenvector continuation (EC) for parameter space exploration and model order reduction (MOR) for extrapolation in frequency space. Contrary to conventional parameterized MOR, we construct these reduced-order models with a parameter-independent resolvent, further reducing the number of required full-space evaluations. Benchmarking against exact diagonalization as the impurity solver for our example case of DMFT calculations for single- and two-band models, MOR+EC reproduces the DMFT-converged impurity GF to an average relative error below 10^−3, with a median wall-time speedup of $9.5−92\times$. This accuracy and efficiency together resolve a fine-grained scan of the impurity occupation as doping is tuned and produce a high-resolution phase diagram of an orbital-selective Mott transition. The reduced-order model also reproduces real- and imaginary-frequency spectra at no additional cost in full-space evaluations. This framework applies broadly to GF-based methods requiring repeated parametric evaluation and high resolution of the frequency axis.
ER -