Abstract
In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum $l=1$ states of a diamond-chain lattice, wherein an effective $\pi$ flux may yield a completely flat single-particle energy landscape. In the weakly-interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.
Highlights
The study of topological materials is a prominent topic in condensed matter physics
As predicted by the analysis of the band structures of the effective models describing the H4 and H3 subspaces, for |U1| − |U2| > 0 the system is in a topological phase characterized by the presence of in-gap edge states in the spectrum, which correspond to the red lines of Fig. 5(a)
The plot (i) displays the spectra corresponding to the interaction parameters {UA/J2 = −0.02, U1/J2 = −0.01, U2/J2 = −0.02}, while (ii) displays the spectra corresponding to the parameters {UA/J2 = −0.02, U1/J2 = −0.02, U2/J2 = −0.01}
Summary
The study of topological materials is a prominent topic in condensed matter physics. One of the main features of these exotic systems is the existence of a bulk-boundary correspondence, which correlates the nontrivial topological indices of the bulk energy bands with the presence of robust edge modes [1]. Due to the effect of the on-site interactions, the total set of states with the two bosons in the lowest single-particle energy bands, which we denote as H, can be divided into the following 4 subspaces according to the values of the self-energy:. This is the subspace of states where the two bosons occupy localized modes separated by two unit cells or more In these configurations there is no overlap between the two particles, and the interaction energy is zero, 0|W−n,iW−m,kHintW−n,†iW−m,†k|0 = 0. Since the states of H2 have double occupancy only on the two common sites of two consecutive plaquettes, the spectrum of this subspace consists of flat bands formed by combinations of states localized in two neighboring plaquettes
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