Mobility edges in $\mathcal{PT}$-symmetric cross-stitch flat band lattices

TL;DR

This paper investigates the existence of mobility edges in a non-Hermitian $ ext{PT}$-symmetric cross-stitch flat band lattice, revealing their role in signaling $ ext{PT}$ symmetry breaking and localization transitions.

Contribution

It provides exact solutions for mobility edges in a $ ext{PT}$-symmetric flat band lattice, linking them to symmetry breaking and localization phenomena.

Findings

Mobility edges are exactly determined in the model.

Mobility edges signal the $ ext{PT}$ symmetry breaking point.

The relationship between localization transition and $ ext{PT}$ symmetry breaking is established.

Abstract

We study the cross-stitch flat band lattice with a $\mathcal{PT}$-symmetric on-site potential and uncover mobility edges with exact solutions. Furthermore, we study the relationship between the $\mathcal{PT}$ symmetry broken point and the localization-delocalization transition point, and verify that mobility edges in this non-Hermitian model is available to signal the $\mathcal{PT}$ symmetry breaking.