  We show that non-Hermitian dynamics generate substantial entanglement in
many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and
show that its phase transition occurs with maximum multiparticle entanglement:
there is full N-particle entanglement at the transition, in contrast to the
Hermitian case. The non-Hermitian model also exhibits more spin squeezing than
the Hermitian model, showing that non-Hermitian dynamics are useful for quantum
metrology. Experimental implementations with trapped ions and cavity QED are
discussed.
