  In the paper, we study the non-Hermitian system under dissipation and give
the effective 2*2 Hamiltonian in the k-space by reducing the N*N Hamiltonian in
the real space for them. It is discovered that the energy band shows an
imaginary line gap. To describe these phenomena, we propose the theory of
"non-Hermitian tearing", in which the tearability we define reveals a
continuous phase transition at the exceptional point. The non-Hermitian tearing
manifests in two forms -- separation of bulk state and decoupling of boundary
state. In addition, we also explore the one-dimensional Su-Schrieffer-Heeger
model and the Qi-Wu-Zhang model under dissipation using the theory of
non-Hermitian tearing. Our results provide a theoretical approach for exploring
the controlling of non-Hermitian physics on topological quantum states.
