Bulk and edge states in Fibonacci-Bose-Hubbard clusters

We study the one- and two-boson energy subspaces of finite open Bose--Hubbard chains with Fibonacci-modulated hopping and zero on-site potential. Their spectra exhibit a hierarchy of bands and gaps, and a critical zero-energy mode for odd lengths, in agreement with prior research. For the singe-excitation subspace we find two families of length-invariant finite-energy states localized at the left cluster boundary. For the two-boson subspace, we report both doublon and separated-pair excitations in the form of Tamm/Shockley states localized near either end. In particular, the right-edge doublon states occur across all Fibonacci generations whereas the left-side states appear every second generation. We check numerically that the second-order perturbation theory accounts well for the structure of the spectrum and the edge states in the doublon subspace in the strong-coupling regime. The results are useful for future explorations of many-body physics beyond numerical tractability, specifically using near-term Josephson quantum simulators.