Bosonization of the Interacting Su-Schrieffer-Heeger Model

We derive the bosonization of the interacting fermionic Su-Schrieffer-Heeger (SSH) model with open boundaries. We use the classical Euler-Lagrange equations of motion of the bosonized theory to compute the density profile of the zero-energy edge mode and observe excellent agreement with numerical results, notably the localization of the mode near the boundaries. Remarkably, we find that repulsive or attractive interactions do not systematically localize or delocalize the edge mode but their effects depend on the value of the staggering parameter. We provide quantitative predictions of these effects on the localization length of the edge mode. Our study shows that bosonization is able to quantitatively describe edge modes of interacting topological one-dimensional systems and pave the way to generalization to other models.