Lattice Improvement in Lattice Effective Field Theory

TL;DR

This paper demonstrates how lattice improvement techniques can systematically reduce errors in lattice effective field theory calculations, specifically for a one-dimensional bosonic system, enhancing future computational accuracy.

Contribution

The study constructs and benchmarks an improved lattice action up to next-to-next-to-leading order, showing errors scale as the fourth power of lattice spacing.

Findings

Errors scale as the fourth power of lattice spacing.

Improved lattice actions increase calculation accuracy.

Benchmarking confirms effectiveness of lattice improvement.

Abstract

Lattice calculations using the framework of effective field theory have been applied to a wide range 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.