Topological bound states in interacting Su–Schrieffer–Heeger rings

Abstract

We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.

Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum

“…In order to circumvent these limitations a third mapping can be introduced, through a basis rotation of (3) (see [43] for details), wherein inversion symmetry and, therefore, a quantized Zak's phase for each band, is recovered. Under this third mapping the system becomes a diamond chain with alternating tunneling amplitudes, whose non-trivial topological nature of the gaps where the edge states lie is explicitly shown in [46,47]. A striking feature of the topology of this model, directly carried over to the original OAM l = 1 model, is that there is no topological transition across the gap closing point, as can be seen by fixing either J 2 or J 3 and varying the other across zero.…”

Corroborating the bulk-edge correspondence in weakly interacting one-dimensional topological insulators

“…As a concrete example of the approach described in the previous sections, here we consider the spinless Su-Schrieffer-Heeger (SSH) model in the presence of electron-electron interaction. Various versions of interacting SSH model has been studied previously and investigated by different methods [42][43][44][45][46]. The topological properties in the noninteracting limit, on the other hand, has been studied experimentally by means of optical lattices [47,48].…”

Interaction-induced topological properties of two bosons in flat-band systems

“…These two-body states, which are stable even for repulsive interactions due to the finite bandwidth of the singleparticle kinetic energy [9], have been observed [10][11][12][13] and extensively analyzed [14][15][16][17][18][19][20][21][22][23][24][25] in optical lattices, and have also been emulated in photonic systems [26,27] and in topolectrical circuits [28]. Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,…”