Lattice methods and the nuclear few- and many-body problem

Abstract

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.

20 pages, 3 figures, Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editors

References in corpus (9)

• Accurate nuclear radii and binding energies from a chiral interaction
• Ab initio alpha-alpha scattering
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Nuclear binding near a quantum phase transition
• Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order
• Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles
• Precise determination of lattice phase shifts and mixing angles
• Chiral effective field theory on the lattice at next-to-leading order
• Scattering cluster wave functions on the lattice using the adiabatic projection method

Cited by in corpus (5)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Systematically Localizable Operators for Quantum Simulations of Quantum Field Theories
• Solving reaction dynamics with quantum computing algorithms
• Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice