Universal conductance of a $\mathcal{PT}$-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.

Figure 1

(a) Formation of the regular light cone as well as the supersonic modes in the density profile $n(x,t)$ for $J_z=-0.3J$. (b) Cuts at a given time along the chain, displaying particles accumulation between the regular and supersonic light cones. (c) Density plot for the current $j(x,t)$. (d) Evolution of the current along the chain. In panels (a) and (c) the white dashed lines represent the world lines for the light cones.

Figure 2

The universal conductance of the PT non-Hermitian Luttinger model indicating the universal behavior predicted in Eq. (1) (blue symbols). The red symbols correspond to the conductance of the Hermitian interacting LL model, consisting in replacing $J_z\to -i{J}_z$ in Eq. (25). The red dashed line represents the fit with the analytical expressions displayed in the legend. The initial state corresponds to a noninteracting model.

Figure 3

Conductance of the PT non-Hermitian Luttinger model, when the initial state is a Hermitian interacting Luttinger liquid. The conductance remains universal when the system is quenched from an interacting state to a non-Hermitian model irrespective on the strength of the initial and post-quench interactions.