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, which 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.
- Received 5 March 2019
- Revised 14 May 2019
DOI:https://doi.org/10.1103/PhysRevA.99.062112
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society