  Dimensionality significantly affects exciton production and condensation.
Despite the report of excitonic instability in one-dimensional materials, it
remains unclear whether these spontaneously produced excitons can form
Bose-Einstein condensates. In this work, we first prove statistically that
one-dimensional condensation exists when the spontaneously generated excitons
are thought of as an ideal neutral Bose gas, which is quite different from the
inability of free bosons to condense. We then derive a general expression for
the critical temperature in different dimensions and find that the critical
temperature increases with decreasing dimension. We finally predict by
first-principles $GW$-BSE calculations that experimentally accessible
single-chain staircase Scandocene and Chromocene wires are an antiferromagnetic
spin-triplet excitonic insulator and a ferromagnetic half-excitonic insulator,
respectively.
