  We show that the bulk-boundary correspondence for topological insulators can
be modified in the presence of non-Hermiticity. We consider a one-dimensional
tight-binding model with gain and loss as well as long-range hopping. The
system is described by a non-Hermitian Hamiltonian that encircles an
exceptional point in momentum space. The winding number has a fractional value
of 1/2. There is only one dynamically stable zero-energy edge state due to the
defectiveness of the Hamiltonian. This edge state is robust to disorder due to
protection by a chiral symmetry. We also discuss experimental realization with
arrays of coupled resonator optical waveguides.
