Characterizing Topological Phase Transition in Non-Hermitian Systems

We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically, such a quantity is used to measure the overall dissimilarity between eigen wavefunctions upon traversing all possible matter states, and confirms the phase boundaries through observing the divergences of both TD and its partial derivatives; we clarify its origin and also offer a theoretical explanation. The method is developed to characterize the non-Hermitian topology in a novel way, and shows its generality and effectiveness in 1D non-Hermitian Kitaev systems, non-Hermitian Hamiltonians under periodic or open boundary conditions, and even generalizable to higher-order topological systems, providing a novel perspective to understand topological physics.