Eur. Phys. J. A (2018) 54: 233
https://doi.org/10.1140/epja/i2018-12676-1

Regular Article - Theoretical Physics

Lattice improvement in lattice effective field theory

¹ Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany
² National Superconducting Cyclotron Laboratory, Michigan State University, 48824, East Lansing, MI, USA
³ Department of Physics, North Carolina State University, 27695, Raleigh, NC, USA
⁴ Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425, Jülich, Germany
⁵ JARA - High Performance Computing, Forschungszentrum Jülich, D-52425, Jülich, Germany
⁶ Tbilisi State University, 0186, Tbilisi, Georgia

^* e-mail: klein@hiskp.uni-bonn.de

Received: 8 October 2018
Accepted: 4 December 2018
Published online: 27 December 2018

Abstract

Lattice calculations using the framework of effective field theory have been applied to a wide range of few-body and many-body systems. One of the challenges of these calculations is to remove systematic errors arising from the nonzero lattice spacing. Fortunately, the lattice improvement program pioneered by Symanzik provides a formalism for doing this. While lattice improvement has already been utilized in lattice effective field theory calculations, the effectiveness of the improvement program has not been systematically benchmarked. In this work we use lattice improvement to remove lattice errors for a one-dimensional system of bosons with zero-range interactions. We construct the improved lattice action up to next-to-next-to-leading order and verify that the remaining errors scale as the fourth power of the lattice spacing for observables involving as many as five particles. Our results provide a guide for increasing the accuracy of future calculations in lattice effective field theory with improved lattice actions.