  It is well known that inversion symmetry in one-dimensional (1D) systems
leads to the quantization of the geometric Zak phase to values of either 0 or
{\pi}. When the system has particle-hole symmetry, this topological property
ensures the existence of zero-energy interface states at the interface of two
bulk systems carrying different Zak phases. In the absence of inversion
symmetry, the Zak phase can take any value and the existence of interface
states is not ensured. We show here that the situation is different when the
unit cell contains multiple degrees of freedom and a hidden inversion symmetry
exists in a subspace of the system. As an example, we consider a system of two
Su-Schrieffer-Heeger (SSH) chains coupled by a coupler chain. Although the
introduction of coupler chain breaks the inversion symmetry of the system, a
certain hidden inversion symmetry ensures the existence of a decoupled
$2\times2$ SSH Hamiltonian in the subspace of the entire system and the two
bands associated with this subspace have quantized Zak phases. These
"quantized" bands in turn can provide topological boundary or interface states
in such systems. Since the entire system has no inversion symmetry, the
bulk-boundary correspondence may not hold exactly. The above is also true when
next-nearest-neighbor hoppings are included. Our systems can be realized
straightforwardly in systems such as coupled single-mode optical waveguides or
coupled acoustic cavities.
