  Excitons in two-dimensional semiconductors provide a novel platform for
fundamental studies of many-body interactions. In particular, dipolar
interactions between spatially indirect excitons may give rise to strongly
correlated phases of matter that so far have been out of reach of experiments.
Here, we show that excitonic few-body systems in atomically thin
transition-metal dichalcogenides undergo a crossover from a Tonks-Girardeau to
a charge-density-wave regime. To this end, we take into account realistic
system parameters and predict the effective exciton-exciton interaction
potential. We find that the pair correlation function contains key signatures
of the many-body crossover already at small exciton numbers and show that
photoluminescence spectra provide readily accessible experimental fingerprints
of these strongly correlated quantum many-body states.
