Hermitian Mapping of Non-Hermitian Topological Properties

This study addresses a fundamental challenge in non-Hermitian topology: establishing a clear correspondence with conventional Hermitian topological frameworks. We develop a universal mapping scheme within the chiral symmetry class that rigorously connects the topological properties of a non-Hermitian system to those of a Hermitian counterpart. By elucidating the origin of the non-Hermitian winding number on the generalized Brillouin zone (GBZ), we trace it to a synchronization condition of zero winding numbers in two complementary subspaces. Based on this insight, we propose a general construction of a chiral-symmetric Hermitian Hamiltonian that fully reproduces the topological features of the original non-Hermitian model. The validity of the mapping is confirmed through the calculation of a real-space topological invariant, the multipole chiral number (MCN), which serves as a direct probe of the bulk topology. Our work not only reveals a key mechanism underlying non-Hermitian topological phases but also provides a universal and practical theoretical pathway for simulating non-Hermitian topological states on established Hermitian platforms.