Bosonization of the interacting Su-Schrieffer-Heeger model

One of the simplest model capturing the key features of topological insulators is the Su-Shrieffer-Heeger (SSH) model which consists of a 1D tight-binding model with alternating bond value. Although the SSH is now considered as a textbook model for topological insulators, the inclusion of interactions in this model remains to this day an open question. In this work, we apply the bosonization procedure to treat interactions in the SSH model with open boundaries. We use the classical Euler-Lagrange equations of motions of the bosonized theory to compute the density profile of the Majorana edge mode in the topological phase. In the non-interacting case, we observe excellent agreement with numerical results obtained from exact diagonalization, notably the exponential localization of the mode near the edges. In the bosonized language, the inclusion of nearest-neighbors interactions amounts to a rescaling of the parameters of the free bosonic Hamiltonian and we derive an explicit formula for the localization length in presence of interactions.