We theoretically investigate the topological properties of a dimerized quasi-one-dimensional (1D) lattice comprised of multilegs $\left(L\right)$ as well as multisublattices $\left(R\right)$. The system has main and subsidiary exchange symmetries. In the basis of the latter one, the system can be divided into $L$ 1D subsystems, each of which corresponds to a generalized ${\mathrm{SSH}}_R$ model having $R$ sublattices and on-site potentials. Chiral symmetry is absent in all subsystems except when the axis of the main exchange symmetry coincides on the central chain. We find that the system may host zero- and finite-energy topological edge states. The existence of a zero-energy edge state requires a certain relation between the number of legs and sublattices. As such, different topological phases, protected by subsystem symmetry, including zero-energy edge states in the main gap, no zero-energy edge states, and zero-energy edge states in the bulk states are characterized. Despite the classification symmetry of the system belongs to BDI symmetry class, but each subsystem falls into either AI or BDI symmetry class.

• Received 18 April 2022
• Accepted 27 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.205111