  Active matter has been intensely studied for its wealth of intriguing
properties such as collective motion, motility-induced phase separation (MIPS),
and giant fluctuations away from criticality. However, the precise connection
of active materials with their equilibrium counterparts has remained unclear.
For two-dimensional (2D) systems, this is also because the experimental and
theoretical understanding of the liquid, hexatic, and solid equilibrium phases
and their phase transitions is very recent. Here, we use self-propelled
particles with inverse-power-law repulsions (but without alignment
interactions) as a minimal model for 2D active materials. A kinetic Monte Carlo
(MC) algorithm allows us to map out the complete quantitative phase diagram. We
demonstrate that the active system preserves all equilibrium phases, and that
phase transitions are shifted to higher densities as a function of activity.
The two-step melting scenario is maintained. At high activity, a critical point
opens up a gas-liquid MIPS region. We expect that the independent appearance of
two-step melting and of MIPS is generic for a large class of two-dimensional
active systems.
