Tight-binding lattices with an oscillating imaginary gauge field

TL;DR

This paper investigates the effects of an oscillating imaginary gauge field on a quantum particle in one-dimensional tight-binding lattices, revealing topology-dependent behaviors including complex spectra and pseudo-Hermitian dynamics.

Contribution

It demonstrates how lattice topology influences non-Hermitian quantum dynamics under a time-periodic imaginary gauge field, showing distinct behaviors in open chains versus rings.

Findings

Open chains exhibit complex quasi-energy spectra due to parametric resonance.

Ring topologies can sustain real quasi-energy spectra and pseudo-Hermitian dynamics.

Large N limit explains behaviors via wave packet propagation.

Abstract

We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of $N$ sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasi energy spectrum via a multiple parametric resonance, in a ring topology (Born-von Karman periodic boundary conditions) an entirely real quasi energy spectrum can be found and the dynamics is pseudo-Hermitian. In the large $N$ limit, parametric instability and pseudo-Hermitian dynamics in the two different lattice topologies are physically explained on the basis of a simple picture of wave packet propagation.