Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model

We investigate the quantum quench dynamics of the interacting Hatano-Nelson model with open boundary conditions using both Abelian bosonization and numerical methods. Specifically, we follow the evolution of the particle density and current profile in real space over time by turning the imaginary vector potential on or off in the presence of weak interactions. Our results reveal spatiotemporal Friedel oscillations in the system with light cones propagating ballistically from the open ends, accompanied by local currents of equal magnitude for both switch-off and -on protocols. Remarkably, the bosonization method accurately accounts for the density and current patterns with a single overall fitting parameter. The continuity equation is satisfied by the long-wavelength part of the density and current, despite the nonunitary time evolution when the Hatano-Nelson term is switched on.

Automated summary

The quantum quench dynamics of the interacting Hatano-Nelson model with open boundary conditions is investigated using Abelian bosonization and numerical methods. The evolution of particle density and current profile in real space over time is followed by turning on or off the imaginary vector potential in the presence of weak interactions. The results show spatiotemporal Friedel oscillations with light cones propagating ballistically from the open ends, accompanied by local currents of equal magnitude for both switching protocols. The bosonization method accurately describes the density and current patterns with a single overall fitting parameter. The continuity equation is satisfied by the long-wavelength part of the density and current, despite the nonunitary time evolution when the Hatano-Nelson term is switched on.