  Neutron star equations of state with strong phase transitions may support
twin stars, hybrid and hadronic stars with the same mass but different tidal
deformabilities. The presence of twin stars in the population of merging
neutron stars produces distinctive gaps in the joint distribution of binary
tidal deformabilities and chirp masses. We analyze a simulated population of
binary neutron star mergers recovered with a network of next-generation (XG)
ground-based gravitational-wave detectors to determine how many observations
are needed to infer, or rule out, the existence of twin stars. Using a
hierarchical inference framework based on a simple parametric twin-star model,
we find that a single week of XG observations may suffice to detect a tidal
deformability difference of several hundred between twins and measure the mass
scale at which twins occur to within a few percent. For less pronounced twins,
XG observations will place a stringent upper bound on the tidal deformability
difference.
