Sublattice signatures of transitions in a $\mathcal{PT}$-symmetric dimer lattice

TL;DR

This paper investigates how a non-Hermitian, $ ext{PT}$-symmetric dimer lattice exhibits distinct $ ext{PT}$-breaking and topological transitions, analyzing their signatures through numerical and analytical methods in state evolution.

Contribution

It provides a combined numerical and analytical study of the signatures of $ ext{PT}$-breaking and topological transitions in a $ ext{PT}$-symmetric dimer lattice.

Findings

Identification of signatures of $ ext{PT}$-breaking transition.

Identification of signatures of topological transition.

Analysis of state evolution on gain and loss sites.

Abstract

Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer lattice consists of dimers with intra-dimer coupling $\nu$, inter-dimer coupling $\nu'$, and balanced gain and loss potentials $\pm i\gamma$ within each dimer. This model undergoes two independent transitions, namely a $\mathcal{PT}$-breaking transition and a topological transition. We numerically and analytically investigate the signatures of these transitions in the time-evolution of states that are initially localized on the gain-site or the loss-site.