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 manybody 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:

 Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
 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:
 AC0205CH11231; SC0017867
 Resource Type:
 Published Article
 Journal Name:
 Proceedings of the National Academy of Sciences of the United States of America
 Additional Journal Information:
 Journal Volume: 115; Journal Issue: 10; Journal ID: ISSN 00278424
 Publisher:
 National Academy of Sciences, Washington, DC (United States)
 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. Tue .
"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 = {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 manybody 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}
}
https://doi.org/10.1073/pnas.1720782115
Web of Science
Figures / Tables:
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