  In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glick
models with alternating couplings between nearest-neighbors sites, which
resembles the Su-Schrieffer-Heeger model. Typical properties of the underlying
models are present in our semiclassical-topological hybrid system, allowing us
to investigate an interplay between semiclassical bifurcations at mean-field
level and topological phases. Our results show that bifurcations of the energy
landscape lead to diverse ordered quantum phases. Furthermore, the study of the
quantum fluctuations around the mean field solution reveals the existence of
nontrivial topological phases. These are characterized by the emergence of
localized states at the edges of a chain with open boundary conditions.
