  Excitonic condensation and superfluidity have recently received a renewed
attention, due to the fabrication of bilayer systems in which electrons and
hole are spatially separated and form stable pairs known as indirect excitons.
Dichalcogenides- and graphene- based bilayers are nowadays built and
investigated, giving access to systems with (i) only spin degeneracy, (ii) spin
and valley degeneracy. Simulation studies performed in the last decade at $T=0$
for simple, model electron-hole bilayers, as function of inter-layer distance
and in-layer carrier density, have revealed in case (i) the formation of
biexcitons in a tiny region of parameter space and in case (ii) the formation
of stable compounds made of 4 electrons and 4 holes (quadriexcitons) in a
sizable region of parameter space. Of some interest is the relation of the
properties of isolated biexcitons (quadriexcitons) and those of their finite
density counterpart. In fact, the isolated biexciton has been repeatedly
studied in the last years with simulations and other techniques. No
simulations, instead, are available to our knowledge for the isolated
quadriexciton, for which we present here results of the first quantum Monte
Carlo (QMC) study. Stability with respect to the dissociation into biexcitons,
and the pair correlations with varying the inter-layer distance $d$ are
discussed.
