Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice

The $N$-flavor interacting Su-Schrieffer-Heeger (i-SSH) model realizable in cold-atoms in an optical lattice is studied. We clarify the relationship between the i-SSH model and the Chiral-Gross-Neveu-Wilson (CGNW) model. Following the previous study of the CGNW model in the high-energy physics community, the groundstate phases of the i-SSH model are investigated and interpreted from the view of the phases of the CGNW model. The interaction effect on the i-SSH model, belonging to the topological BDI class, is grasped by following the view of the dynamical breakdown of chiral symmetry in the CGNW model. Furthermore, we compare the large-$N$ groundstate phase diagram with that of the $N=1$ case obtained by exact diagonalization and then propose a table-top cold-atom quantum simulator to test the model.