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Title: Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory

Abstract

Significance Many-body perturbation theory is one of the pillars of quantum many-body physics and has been used extensively to predict ground-state and excited-state electronic properties of real materials in the past few decades. Nonetheless, few practically used methods in many-body perturbation theory have been justified on a rigorous basis. We present a variational formalism that can be used for the rigorous study of a number of many-body perturbation methods in Euclidean lattice field theory. In particular, this perspective allows us to justify the widely used bold Feynman diagrammatic expansion, without relying on formal arguments such as partial resummation of Feynman diagrams to infinite order.

Authors:
 [1];  [2]
  1. Department of Mathematics, University of California, Berkeley, CA 94720,, Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
  2. Department of Mathematics, University of California, Berkeley, CA 94720,
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1421895
Alternate Identifier(s):
OSTI ID: 1485086
Grant/Contract Number:  
SC0017867; AC02-05CH11231
Resource Type:
Journal Article: Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 115 Journal Issue: 10; Journal ID: ISSN 0027-8424
Publisher:
Proceedings of the National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Lin, Lin, and Lindsey, Michael. Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory. United States: N. p., 2018. Web. doi:10.1073/pnas.1720782115.
Lin, Lin, & Lindsey, Michael. Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory. United States. https://doi.org/10.1073/pnas.1720782115
Lin, Lin, and Lindsey, Michael. 2018. "Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory". United States. https://doi.org/10.1073/pnas.1720782115.
@article{osti_1421895,
title = {Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory},
author = {Lin, Lin and Lindsey, Michael},
abstractNote = {Significance Many-body perturbation theory is one of the pillars of quantum many-body physics and has been used extensively to predict ground-state and excited-state electronic properties of real materials in the past few decades. Nonetheless, few practically used methods in many-body perturbation theory have been justified on a rigorous basis. We present a variational formalism that can be used for the rigorous study of a number of many-body perturbation methods in Euclidean lattice field theory. In particular, this perspective allows us to justify the widely used bold Feynman diagrammatic expansion, without relying on formal arguments such as partial resummation of Feynman diagrams to infinite order.},
doi = {10.1073/pnas.1720782115},
url = {https://www.osti.gov/biblio/1421895}, journal = {Proceedings of the National Academy of Sciences of the United States of America},
issn = {0027-8424},
number = 10,
volume = 115,
place = {United States},
year = {Tue Feb 20 00:00:00 EST 2018},
month = {Tue Feb 20 00:00:00 EST 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at https://doi.org/10.1073/pnas.1720782115

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: Bold diagrams for the first-order (A and B) and second-order (C and D) contribution to the self-energy for interaction of the form Eq. 10.

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Works referenced in this record:

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Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.