  Identifying topological phases for a strongly correlated theory remains a
non-trivial task, as defining order parameters, such as Berry phases, is not
straightforward. Quantum information theory is capable of identifying
topological phases for a theory that exhibits quantum phase transition with a
suitable definition of order parameters that are related to different
entanglement measures for the system. In this work, we study entanglement
entropy for a bi-layer SSH model, both in the presence and absence of Hubbard
interaction and at varying interaction strengths. For the free theory, edge
entanglement acts as an order parameter, which is supported by analytic
calculations and numerical (DMRG) studies. We calculate the symmetry-resolved
entanglement and demonstrate the equipartition of entanglement for this model
which itself acts as an order parameter when calculated for the edge modes. As
the DMRG calculation allows one to go beyond the free theory, we study the
entanglement structure of the edge modes in the presence of on-site Hubbard
interaction for the same model. A sudden reduction of edge entanglement is
obtained as interaction is switched on. The explanation for this lies in the
change in the size of the degenerate subspaces in the presence and absence of
interaction. We also study the signature of entanglement when the interaction
strength becomes extremely strong and demonstrate that the edge entanglement
remains protected. In this limit, the energy eigenstates essentially become a
tensor product state, implying zero entanglement. However, a remnant entropy
survives in the non-trivial topological phase which is exactly due to the
entanglement of the edge modes.
