Real-Frequency Diagrammatics with Pole Representations
Abstract
Finite-temperature many-body theories are typically formulated in imaginary time, where they are amenable to efficient numerical treatment. However, the extraction of spectral properties from the imaginary axis is difficult and requires numerical analytic continuation, while a direct formulation on the real axis requires prohibitively expensive numerical quadrature. In this paper, we represent the objects of many-body perturbation theory using systematically improvable pole and moment expansions and develop the corresponding framework for evaluating diagrammatic contributions directly on the real axis. We introduce a controlled recompression procedure that prevents the proliferation of poles under algebraic and diagrammatic operations. We benchmark the approach on paradigmatic quantum impurity problems and apply it to self-consistent calculations of the uniform electron gas. The resulting spectral quantities converge systematically towards numerical accuracy. This work provides a practical framework for controlled and systematically improvable calculations of spectral quantities within diagrammatic many-body theories, including self-consistent conserving approaches.
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BibTeX
@misc{farid2026realfrequency,
title = {{Real-Frequency Diagrammatics with Pole Representations}},
author = {Rayan Farid and Lei Zhang and Aiman Al-Eryani and Agnieszka Jażdżewska and Emanuel Gull},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26703},
eprint = {2609.26703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26703},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Real-Frequency Diagrammatics with Pole Representations
AU - Rayan Farid
AU - Lei Zhang
AU - Aiman Al-Eryani
AU - Agnieszka Jażdżewska
AU - Emanuel Gull
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26703
UR - https://arxiv.org/abs/2609.26703
AB - Finite-temperature many-body theories are typically formulated in imaginary time, where they are amenable to efficient numerical treatment. However, the extraction of spectral properties from the imaginary axis is difficult and requires numerical analytic continuation, while a direct formulation on the real axis requires prohibitively expensive numerical quadrature. In this paper, we represent the objects of many-body perturbation theory using systematically improvable pole and moment expansions and develop the corresponding framework for evaluating diagrammatic contributions directly on the real axis. We introduce a controlled recompression procedure that prevents the proliferation of poles under algebraic and diagrammatic operations. We benchmark the approach on paradigmatic quantum impurity problems and apply it to self-consistent calculations of the uniform electron gas. The resulting spectral quantities converge systematically towards numerical accuracy. This work provides a practical framework for controlled and systematically improvable calculations of spectral quantities within diagrammatic many-body theories, including self-consistent conserving approaches.
ER -