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Lattice Methods and the Nuclear Few- and Many-Body Problem

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An Advanced Course in Computational Nuclear Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 936))

Abstract

This chapter builds upon the review of lattice methods and effective field theory of the previous chapter. We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.

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Acknowledgements

The author is grateful for discussions with Amy Nicholson and Morten Hjorth-Jensen. He is also greatly indebted to his collaborators Jose Alarcón, Dechuan Du, Serdar Elhatisari, Evgeny Epelbaum, Nico Klein, Hermann Krebs, Timo Lähde, Ning Li, Bing-nan Lu, Thomas Luu, Ulf-G. Meißner, Alexander Rokash, and Gautam Rupak. Partial financial support provided by the U.S. Department of Energy (DE-FG02-03ER41260). Computational resources were provided by the Jülich Supercomputing Centre.

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Authors and Affiliations

  1. Department of Physics, North Carolina State University, Raleigh, NC, 27695, USA

    Dean Lee

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  1. Dean Lee
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Correspondence to Dean Lee .

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Editors and Affiliations

  1. National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA

    Morten Hjorth-Jensen

  2. INFN, Laboratori Nazionali di Frascati, Frascati Roma, Italy

    Maria Paola Lombardo

  3. Department of Physics, University of Arizona, Tucson, Arizona, USA

    Ubirajara van Kolck

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Lee, D. (2017). Lattice Methods and the Nuclear Few- and Many-Body Problem. In: Hjorth-Jensen, M., Lombardo, M., van Kolck, U. (eds) An Advanced Course in Computational Nuclear Physics. Lecture Notes in Physics, vol 936. Springer, Cham. https://doi.org/10.1007/978-3-319-53336-0_6

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