  It is known that effects of dissipation or measurement backreaction in
postselected quantum trajectories are described by non-Hermitian Hamiltonian,
but their consequences in real-time dynamics of many-body systems are yet to be
elucidated. Through a study of a non-Hermitian Hubbard model, we reveal a novel
dissipation-induced dynamical phase transition in postselected quantum
trajectories, where time controls the strength of postselection and becomes the
intrinsic parameter inducing the phase transition. Our findings are testable in
ultracold atom experiments and may open a new avenue in the dissipative
engineering of quantum systems.
