  Dramatically different from the Hermitian systems, the conventional
Bulk-Boundary Correspondence (BBC) is broken in the non-Hermitian systems. In
this article, we use edge entanglement entropy to characterize the topological
properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free
Fermions, we study the scaling behavior of entanglement entropy and demonstrate
that the edge entanglement entropy is a good indicator to delimit different
phases of non-Hermitian systems. We further generalize the edge entanglement
entropy to the non-Hermitian interacting Hubbard chain, and obtain the
topological phase diagram in the plane of interaction and non-Hermitian hopping
amplitudes. It is found that the Hubbard interaction diminishes and weakens the
breakdown of Bulk-Boundary Correspondence, which eventually disappears at some
critical value of interaction.
