  As the simplest non-Fermi liquids, orthogonal metals have gapped
single-particle excitations but show normal metallic behaviors in thermodynamic
and transport quantities. Such an exotic metallic state could be realized in a
Hubbard model with pair-hopping term. However, it is difficult to solve this
model in higher dimension, here we focus on its one-dimension version, in which
a powerful U(1) abelian bosonization technique is available to capture
\textit{analytically} its universal low-energy physics. It is found that the
one-dimensional system is unable to provide an appropriate precursor for the
desirable orthogonal metals in higher dimension and the occurrence of the
featureless orthogonal metallic phase needs \textit{at least} a
quasi-one-dimensional multi-leg ladder model. Nevertheless, two interesting
quantum liquid phases are identified for the present one-dimensional model,
namely, pair-density wave (PDW) state and pair-superconducting (PSC) state. The
former describes the charge-density-wave order of cooper pairs while the latter
shows the superfluidity of two cooper pairs. Needing not any explicit
calculation, these two phases could have further implications in the
two-dimensional case, namely, the PDW state may give rise to quantum electron
liquid crystal states, which is believed to be responsible for the complex
pseudogap phase in cuprate, and the PSC state with charge 4e can be related to
certain nematic superconducting state. These predications call for further
investigation on this model in higher dimension by available analytical methods
and/or numerical calculations.
