# Topological Phase Transition of A Non-Hermitian Crosslinked Chain

## TL;DR

This paper investigates the topological phase transition in a non-Hermitian crosslinked chain, revealing phase diagrams, exceptional points, and robust edge states influenced by gain and loss, with potential photonic implementations.

## Contribution

It provides an analytical phase diagram based on winding numbers for non-Hermitian chains and explores the topological features induced by gain and loss.

## Key findings

- Phase diagram derived analytically using winding number
- Edge states remain stable across long chains and are immune to disorder
- Topological phase boundaries coincide with exceptional point surfaces

## Abstract

Non-Hermiticity enriches the contents of topological classification of matter including exceptional points, bulk-edge correspondence and skin effect. Gain and loss can be described by imaginary diagonal elements in Hamiltonians and the topological phase transition for a crosslinked chain in the presence of such non-Hermiticity is investigated in this work. We obtain the phase diagram in term of a winding number analytically. The boundaries of the phases coincide with the surfaces of exceptional points in the parameter space. The topologically original edge states locating mainly at the joints between domains of different phases hold on even for the long chain. The non-Hermitian topological feature can also be reflected by vortex structures in the vector fields of complex eigenenergies and expected values of Pauli matrices or the trajectories of these quantities. This model can be implemented in coupled waveguides or photonic crystals. And the edge states are immune to various kinds of disorders until the topological phase transition occurs. This work benefits our insight into the influence of gain and loss on the topological phase of matter.