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

Abstract

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 spatio-temporal 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 non-unitary time evolution when the Hatano-Nelson term is switched on.

9 pages, 4 figures

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• Measurement-induced symmetry restoration and quantum Mpemba effect
• Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
• Orthogonality catastrophe beyond bosonization from post-selection
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model