  Indirect excitons -- pairs of electrons and holes spatially separated in
semiconductor bilayers or quantum wells -- are known to undergo Bose-Einstein
condensation and to form a quantum fluid. Here we show that this superfluid may
crystallize upon compression. However, further compression results in quantum
melting back to a superfluid. This unusual behavior is explained by the
effective interaction potential between indirect excitons which strongly
deviates from a dipole potential at small distances due to many-particle and
quantum effects. Based on first principle path integral Monte Carlo
simulations, we compute the complete phase diagram of this system and predict
the relevant parameters necessary to experimentally observe exciton
crystallization in semiconductor quantum wells.
