Interactions from chiral effective field theory have been successfully
employed in a broad range of \textit{ab initio} calculations of nuclei and
nuclear matter, but it has been observed that most results of few- and
many-body calculations experience a substantial residual regulator and cutoff
dependence. In this work, we investigate the behavior of local chiral
potentials at leading order under variation of the cutoff scale for different
local regulators. When varying the cutoff, we require that the resulting
interaction produces no spurious bound states in the deuteron channel. We find
that, for a particular choice of leading-order operators, nucleon-nucleon phase
shifts and the deuteron ground-state energy converge to cutoff-independent
plateaus, for all regulator functions we investigate. This observation may
enable improved calculations with chiral Hamiltonians that also include
three-nucleon interactions.Comment: 10 pages, 6 figures, published versio