  We theoretically investigate Majorana zero modes emerging in an anisotropic
XY spin chain with second neighbor interactions. The spin chain is
mathematically equivalent to the Kitaev chain composing of spinless fermions if
only nearest-neighbor interactions are considered. Recent studies on the Kitaev
chain with long-ranged interactions, have presented coexistence of several
Majorana zero modes. Investigating the topological phase diagram of the
anisotropic XY spin chain with second neighbor interactions, we find
coexistence of several Majorana zero modes similar to the Kitaev chain.
However, we confirm that one of zero modes is restricted into a Hilbert
subspace. The mode is regarded as a so-called weak zero mode that should
exhibit thermodynamical properties different from a (strong) zero mode
appearing in the whole Hilbert space. Since the quantum statistics of spin is
the same as a hard-core boson, we expect an experimental realization of the
weak mode in not only quantum spin materials but also optical lattices.
