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 ground-state phases of the i-SSH model are investigated and interpreted from the viewpoint 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-$N$ ground-state phase diagram with that of the $N=1$ case obtained by exact diagonalization, and then we propose a tabletop cold-atom quantum simulator to test the model.

Figure 1

Large-$N$ phase diagram: (a) type-I i-SSH model, (b) type-II i-SSH model. For both cases, $J_2=1$ and three phases appear: the BI phase, the BDI-SPT phase (for odd $N$ case), and the Aoki phase.

Figure 2

$N=1$ phase structures obtained by exact diagonalization: (a) the type-I i-SSH model and (b) the type-II i-SSH model. For both cases, $J_2=1$.

Figure 3

Implementation scheme using cold atoms in an optical lattice: (a) the type-I i-SSH model, (b) the type-II i-SSH model. In the type-I case, the interaction $V_{\mathrm{I}}$ appears as on-site $s$-wave scattering interaction $U_{eg}$ between the different internal states of fermionic atoms. In the type-II case, the interaction $V_{\mathrm{II}}$ is implemented as long-range DDI $U_d$ using a dipolar fermionic atom.