Condensate states in Fermi and Bose-Hubbard ladders

TL;DR

This paper explores condensate states in Fermi and Bose-Hubbard ladders, revealing their similarities through pair states and analyzing the effects of next-nearest-neighbor hopping.

Contribution

It constructs exact condensate-pair eigenstates for Fermi ladders and shows how they relate to hardcore boson states, highlighting the role of spectrum generating algebra.

Findings

Fermi and hardcore boson pair states can take the same form under certain conditions.

Exact eigenstates for Fermi ladders are constructed using SU(2) symmetry.

Next-nearest-neighbor hopping influences the condensate states' dynamic response.

Abstract

Although neither hardcore 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 hardcore 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 hardcore boson counterpart can be simply obtained by replacing fermionic operators with hardcore 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 hardcore bosons, but also a possible mechanism of Hilbert-space fragmentation.