Band topology and symmetry in pseudo-Hermitian systems

Abstract

Pseudo-Hermiticity ramifies novel symmetries and enriches unique topological phases distinct from existing non-Hermitian frameworks. Here, we introduce new types of pseudo-Hermitian models across various spatial dimensions, constructed based on the q-deformed Clifford algebra. Each model preserves specific symmetries, and we characterize their band topology via (Abelian and non-Abelian) quantum metric and tensor Berry connections. Concrete relations between quantum metric, Berry curvature, and simple connections between topological invariants and quantum volume are established. Interestingly, these pseudo-Hermitian systems have different geometries and symmetries compared to their Hermitian counterparts, while maintaining the same band topology. We show that the emergence of the non-Hermitian skin effect in these models is a consequence of pseudo-Hermiticity breakdown. Finally, we modify their phase diagram using non-Bloch band theory when various open boundary conditions are imposed. Moreover, we propose a practical scheme for implementing these pseudo-Hermitian models in the dilated Hermitian Hamiltonian. Our work provides a systematic theoretical framework for a comprehensive and essential understanding of the concept of topology and symmetry in such systems.