  A crowd of nonequilibrium entities can show phase transition behaviors that
are prohibited in conventional equilibrium setups. An interesting question is
whether similar activity-driven phase transitions also occur in pure quantum
systems. Here we introduce a minimally simple quantum many-body model that
undergoes quantum phase transitions induced by non-Hermiticity. The model is
based on a classical anisotropic lattice gas model that undergoes
motility-induced phase separation (MIPS), and the quantum phase diagram
includes other active phases such as the flocking phase. The quantum phase
transitions, which in principle can be tested in ultracold atom experiments, is
also identified as the transitions of dynamical paths in the classical kinetics
upon the application of biasing fields. This approach sheds light on the useful
connection between classical nonequilibrium kinetics and non-Hermitian quantum
physics.
