Universal conductance of a PT -symmetric Luttinger liquid after a quantum quench

We study the nonequilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular light cone, we find a universal conductance ${e}²/h$, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution with a Hermitian LL Hamiltonian, the conductance is heavily renormalized by the Hermitian interaction as ${e}²/hK$ with $K$ the LL parameter. Our analytical results are tested numerically, confirming the universality of the conductance in the non-Hermitian realm.