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

Abstract

The Luttinger–Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green’s function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger–Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger–Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger–Ward functional, the free energy can be variationally minimized with respect to Green’s functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.

Authors:
;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (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:
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. doi:10.1073/pnas.1720782115.
Lin, Lin, and Lindsey, Michael. Tue . "Variational structure of Luttinger–Ward formalism and bold diagrammatic expansion for Euclidean lattice field theory". United States. doi: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 = {The Luttinger–Ward functional was proposed more than five decades ago and has been used to formally justify most practically used Green’s function methods for quantum many-body systems. Nonetheless, the very existence of the Luttinger–Ward functional has been challenged by recent theoretical and numerical evidence. We provide a rigorously justified Luttinger–Ward formalism, in the context of Euclidean lattice field theory. Using the Luttinger–Ward functional, the free energy can be variationally minimized with respect to Green’s functions in its domain. We then derive the widely used bold diagrammatic expansion rigorously, without relying on formal arguments such as partial resummation of bare diagrams to infinite order.},
doi = {10.1073/pnas.1720782115},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 10,
volume = 115,
place = {United States},
year = {2018},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1720782115

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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    Figures / Tables found in this record:

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