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Lattice Monte Carlo

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Nuclear Lattice Effective Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 957))

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Abstract

Thus far, we have developed the path integral and transfer matrix in Chap. 3 and shown how to apply this formalism to the two-nucleon and three-nucleon forces in NLEFT in Chap. 4. In Chap. 5, we have discussed the calculation of observables in the two- and three-nucleon sectors, and shown how these can be used to fix the free parameters of the NLEFT interactions, which allows the theory to be predictive for A ≥ 4. However, we are still faced with the difficulty that most analytical and numerical methods become impractical for the multi-nucleon problem (for systems of a realistic size) due to adverse exponential scaling of the computational effort with nucleon number A. In this chapter, we shall establish viable computational methods for A ≥ 4 which, given sufficiently realistic nuclear interactions, can be applied to a large range of heavier nuclei as well. In the Euclidean time projection technique, the energy eigenvalues and wave functions of the low-lying spectrum of the Hamiltonian are computed by repeatedly operating on a suitably chosen “trial state” by the operator \(\exp (-\delta H)\), which acts as a “low-energy filter”.

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Authors and Affiliations

  1. Institute for Advanced Simulation and Institute of Nuclear Physics, Forschungszentrum Jülich, Jülich, Germany

    Timo A. Lähde & Ulf-G. Meißner

  2. Helmholtz-Institut für Strahlen-und Kernphysik (Theorie), University of Bonn, Bonn, Germany

    Ulf-G. Meißner

Authors
  1. Timo A. Lähde
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  2. Ulf-G. Meißner
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Lähde, T.A., Meißner, UG. (2019). Lattice Monte Carlo. In: Nuclear Lattice Effective Field Theory. Lecture Notes in Physics, vol 957. Springer, Cham. https://doi.org/10.1007/978-3-030-14189-9_6

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