  For noninteracting Weyl semimetals (WSMs), Fermi-arc surface states can arise
when there exist gapless Weyl nodes in the bulk single-particle spectrum.
However, in the presence of electronic correlations, it is not clear whether
this bulk-boundary correspondence still holds or not. Recently, novel
correlated phases are predicted to appear in WSMs with long-ranged
interactions, in which the bulk Weyl nodes can be gapped but without destroying
their topological properties. Here, we explore the fate of the Fermi-arc states
under the influence of such long-ranged interactions. After mapping the system
onto a one-dimensional interacting Su-Schrieffer-Heeger (SSH) model with two
open ends, we employ numerical exact diagonalizations to address the issue
whether the Fermi-arc states will be modified. By extrapolating our data to the
thermodynamic limit, we find that the zero-energy edge states of the
corresponding SSH model still exist for those momenta giving the noninteracting
Fermi-arc states. Moreover, this observation applies to both the
single-particle and the collective edge excitations. Since the locus of these
edge states constitutes the Fermi arcs, the robustness of the Fermi-arc states
against long-ranged interactions is thus demonstrated. In particular, the Fermi
arcs of single-particle nature can survive even when the single-particle gaps
at the Weyl nodes are opened by interactions. Our results illustrate the
subtlety in identifying the topological phases of interacting WSMs and show the
limitation of the approaches simply by examining the nodal structure of the
single-particle spectrum.
