  We obtain the numerical ground state of a one-dimensional ladder model with
the upper and lower chains occupied by spatially-separated electrons and holes,
respectively. Under charge neutrality, we find that the excitonic bound states
are always formed, i.e., no finite regime of decoupled electron and hole plasma
exists at zero temperature. The system either behaves like a bosonic liquid or
a bosonic crystal depending on the inter-chain attractive and intra-chain
repulsive interaction strengths. We also provide the detailed excitonic phase
diagrams in the intra- and inter-chain interaction parameters, with and without
disorder. We also comment on the corresponding two-dimensional electron-hole
bilayer exciton condensation.
