Condensate states in Fermi and Bose-Hubbard ladders
Phys. Rev. B 114, 055134 – Published 31 July, 2026
DOI: https://doi.org/10.1103/2n38-63nt
Abstract
Although neither hard-core bosons nor fermions can occupy the same single-site state, they still obey different statistics, resulting in distinct many-particle quantum states, such as condensate states versus Fermi-liquid states. However, when only pair states are considered, the two can take the same form, since a local hard-core Bose pair and a Fermi pair obey the same statistics. In this work we demonstrate this by studying both Fermi and Bose extended Hubbard ladders, which can be realized experimentally in synthetic atomic ladders. A set of exact condensate-pair eigenstates for the Fermi ladder is constructed under SU(2) symmetry and can then be obtained by the spectrum generating algebra. The corresponding hard-core boson counterpart can be simply obtained by replacing fermionic operators with hard-core bosonic ones. Nevertheless, the boson-pair eigenstates are associated not with symmetry but with the restricted spectrum generating algebra. We also investigate the effect of next-nearest-neighbor hopping on the condensate states through numerical simulations of the dynamic response. The conclusions can be extended to a two-layer system. Our result reveals not only the resemblance of fermions to hard-core bosons, but also a possible mechanism of Hilbert-space fragmentation.
