  Motivated by the recently discovered incompressible insulating phase in the
bilayer graphene exciton experiment [arXiv:2306.16995], we study using
bosonization two Coulomb-coupled spinless quantum wires and examine the
possibility of realizing the similar phenomenology in one dimension. We explore
the possible phases as functions of $k_{F}$'s and interactions. We show that an
incompressible insulating phase can arise for two lightly doped electron-hole
quantum wires (i.e., $k_{F1}=-k_{F2}$ and small $|k_{F1}|$) due to strong
interwire interactions. Such an insulating phase forms a parity-even
wire-antisymmetric charge density wave without interwire phase coherence, which
melts to a phase allowing for a perfect negative drag upon heating. The
finite-temperature response is qualitatively consistent with the ``exciton
solid'' phenomenology in the bilayer graphene exciton experiment.
