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In this work we study a one-dimensional lattice of Lipkin-Meshkov-Glickmodels with alternating couplings between nearest-neighbors sites, whichresembles the Su-Schrieffer-Heeger model. Typical properties of the underlyingmodels are present in our semiclassical-topological hybrid system, allowing usto investigate an interplay between semiclassical bifurcations at mean-fieldlevel and topological phases. Our results show that bifurcations of the energylandscape lead to diverse ordered quantum phases. Furthermore, the study of thequantum fluctuations around the mean field solution reveals the existence ofnontrivial topological phases. These are characterized by the emergence oflocalized states at the edges of a chain with open boundary conditions.

Semiclassical bifurcations and topological phase transitions in a one-dimensional lattice of coupled Lipkin-Meshkov-Glick models