Multihole edge states in Su-Schrieffer-Heeger chains with interactions

We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t(1) and t(2). Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V/t(2) versus t(1)/t(2) phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and nontrivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a noninteracting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of edge states of topological origin in the equivalent chain can be readily identified, as well as their correspondence to the original two-hole states. Of these states only some, identified by us, are protected and, therefore, truly topological. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).