Bulk and edge states in Fibonacci-Bose-Hubbard clusters
Abstract
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.
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BibTeX
@misc{fedorov2026bulk,
title = {{Bulk and edge states in Fibonacci-Bose-Hubbard clusters}},
author = {G. P. Fedorov and E. E. Konopleva and O. V. Astafiev},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04777},
eprint = {2611.04777},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04777},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bulk and edge states in Fibonacci-Bose-Hubbard clusters
AU - G. P. Fedorov
AU - E. E. Konopleva
AU - O. V. Astafiev
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04777
UR - https://arxiv.org/abs/2611.04777
AB - 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.
ER -