Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model

TL;DR

This paper investigates the slow approach to adiabaticity in a non-Hermitian many-body system, revealing how complex energies and oscillations influence adiabatic dynamics and identifying conditions for shortcuts.

Contribution

It demonstrates the slow damping of non-adiabatic effects in the interacting Hatano-Nelson model and uncovers a natural shortcut to adiabaticity without auxiliary controls.

Findings

Energy becomes complex during the ramp.

Decay of non-adiabatic effects scales as τ^{-1}.

Shortcut to adiabaticity occurs at specific ramp times.

Abstract

We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the density imbalance are analyzed using bosonization and exact diagonalization. The energy becomes complex valued, despite the instantaneous Hamiltonian having the same real spectrum throughout. The adiabatic limit is approached very slowly through damped oscillations. The decay scales with $\tau^{-1}$ with $\tau$ the ramp duration, while the oscillation period is $2L/v$ with $v$ the Fermi velocity and $L$ the system length. Yet, without the need for auxiliary controls, a shortcut to adiabaticity is found for ramp times commensurate with the period. Our work highlights the intricate interplay of adiabaticity and non-Hermitian many-body physics.