  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.
