  Symmetries play a major role in identifying topological phases of matter and
in establishing a direct connection between protected edge states and
topological bulk invariants via the bulk-boundary correspondence.
One-dimensional lattices are deemed to be protected by chiral symmetry,
exhibiting quantized Zak phases and protected edge states, but not for all
cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model
with broken chiral symmetry by engineering one-dimensional zigzag photonic
lattices, where the long-range hopping breaks chiral symmetry but ensures the
existence of inversion symmetry. By the averaged mean displacement method, we
detect topological invariants directly in the bulk through the continuous-time
quantum walk of photons. Our results demonstrate that inversion symmetry
protects the quantized Zak phase, but edge states can disappear in the
topological nontrivial phase, thus breaking the conventional bulk-boundary
correspondence. Our photonic lattice provides a useful platform to study the
interplay among topological phases, symmetries, and the bulk-boundary
correspondence.
