  In this paper, we show that the introduction of long-range hoppings in 1D
topological insulator models implies that different possibilities of site
indexing must be considered when determining the bulk topological invariants in
order to avoid the existence of hidden symmetries. The particular case of the
extended SSH chain is addressed as an example where such behavior occurs. In
this model, the introduction of long-range hopping terms breaks the bipartite
property and a band inversion occurs in the band structure as the relative
values of the hopping terms change, signaling a crossover between hopping
parameter regions of "influence" of different chiral symmetries. Furthermore,
edge states become a linear combination of edge-like states with different
localization lengths and reflect the gradual transition between these different
chiral symmetries.

Mesoscale and Nanoscale Physics