  A Luttinger liquid (LL) describes low energy excitations of many interacting
one dimensional systems, and exhibits universal response both in and out of
equilibrium. We analyze its behaviour in the non-hermitian realm after quantum
quenching to a PT-symmetric LL by focusing on the fermionic single particle
density matrix. For short times, we demonstrate the emergence of unique
phenomena, characteristic to non-hermitian systems, that correlations propagate
faster than the conventional maximal speed, known as the Lieb-Robinson bound.
These emergent supersonic modes travel with velocities that are multiples of
the conventional light-cone velocity. This behaviour is argued to be generic
for correlators in non-hermitian systems. In the long time limit, we find
typical LL behaviour, extending the LL universality to the non-equilibrium
non-hermitian case. Our analytical results are benchmarked numerically and
indicate that the dispersal of quantum information is much faster in
non-hermitian systems.
