Renormalization of a Contact Interaction on a Lattice

Abstract

Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme. We explain how to tune the coefficient of a contact interaction between non-relativistic particles on a discretized space in 1, 2, and 3 spatial dimensions such that we can remove all discretization artifacts. By taking advantage of a latticized Lüscher zeta function, we can achieve a momentum-independent scattering amplitude at any finite lattice spacing.

Comments: Data & code provided at https://github.com/ckoerber/luescher-nd (release v1.0.0). Upload v2 added references