# Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling

## TL;DR

This paper explores how asymmetric coupling in non-Hermitian systems induces phase transitions and eigenstate localization, revealing the roles of imaginary gauge fields and flux in these phenomena.

## Contribution

It demonstrates the connection between asymmetric coupling, imaginary gauge fields, and non-Hermitian phase transitions and localization, including effects in systems with and without translation invariance.

## Key findings

- Imaginary gauge fields induce non-Hermitian phase transitions in closed systems.
- Asymmetric coupling causes eigenstate localization in open boundary systems.
- Imaginary magnetic flux does not always lead to phase transitions in non-translation-invariant systems.

## Abstract

We investigate a uniformly coupled non-Hermitian system with asymmetric coupling amplitude. The asymmetric coupling equals to a symmetric coupling threaded by an imaginary gauge field. In a closed configuration, the imaginary gauge field leads to an imaginary magnetic flux, which induces a non-Hermitian phase transition. For an open boundary, the imaginary gauge field results in an eigenstate localization. The eigenstates under Dirac and biorthogonal norms and the scaling laws are quantitatively investigated to show the affect of asymmetric coupling induced one-way amplification. However, the imaginary magnetic flux does not inevitably induce the non-Hermitian phase transition for systems without translation invariance, this is elucidated from the non-Hermitian phase transition in the non-Hermitian ring with a single coupling defect. Our findings provide insights into the non-Hermitian phase transition and one-way localization.