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

TL;DR

This paper investigates the non-equilibrium transport properties of a PT-symmetric Luttinger liquid after a quantum quench, revealing a universal conductance unaffected by PT-symmetric interactions, contrasting with hermitian cases.

Contribution

It demonstrates the universality of conductance in a PT-symmetric Luttinger liquid post-quench, contrasting with the renormalized conductance in hermitian systems, supported by analytical and numerical analysis.

Findings

Universal conductance of e^2/h in PT-symmetric LL

Conductance remains unaffected by PT-symmetric interactions

Hermitian LL conductance is renormalized by interaction strength

Abstract

We study the non-equilibrium 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 lightcone, 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.