Topology of a parity-time symmetric non-Hermitian rhombic lattice

We investigate the topological properties of a trimerized parity-time ( \mathcalPT) symmetric non-Hermitian rhombic lattice. Although the system is \mathcalPT-symmetric, the topology is not inherited from the Hermitian lattice; in contrast, the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices. The bulk-boundary correspondence is valid and the Bloch bulk captures the band topology. Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach. In addition, the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice. Our findings reveal the topological properties of the \mathcalPT-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.