Symmetry protected topological phases characterized by isolated exceptional points

Exceptional points (EPs) associated with the coalescence of eigenstates in non-Hermitian systems have many exotic features. The EPs are generally sensitive to system parameters; here we report symmetry protected isolated EPs in the Brillouin zone (BZ) of a two-dimensional non-Hermitian bilayer square lattice. Protected by symmetry, the isolated EPs only move, merge, and split in the BZ. The average values of Pauli matrices under the eigenstate of the system's Bloch Hamiltonian define a real planar vector field, the topological defects of which are isolated EPs associated with vortices. The winding number characterizes the vortices and reveals the topological properties of the non-Hermitian system. Different topological phases correspond to different EP configurations, which are unchanged unless topological phase transition occurs accompanying the EPs merging or splitting.