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.
Highlights
The parity-time (PT ) symmetry confinement enables a purely real spectrum of the non-Hermitian system [1,2,3,4,5,6,7,8]
To better understand the influence of asymmetric coupling and the imaginary gauge field, we investigate the biorthogonal norm of the eigenstates
The averaged biorthogonal inverse participation ratio (IPR) is inversely proportional to the system size, which implies that the eigenstate is extended and reveals that the asymmetric coupling induces a gauge field under the biorthogonal norm
Summary
The parity-time (PT ) symmetry confinement enables a purely real spectrum of the non-Hermitian system [1,2,3,4,5,6,7,8]. The asymmetric coupling induces all the eigenstates localized at the system boundary, which is called the non-Hermitian skin effect [82,83,84,85,86,87,88,89]. The asymmetric coupling effectively generates a gauge invariant imaginary field; the imaginary gauge field in a closed area induces an imaginary magnetic flux, which does not inevitably result in a non-Hermitian phase transition, in particular, for the non-Hermitian systems that are not translation invariant. This is elucidated through a non-Hermitian nonuniform ring system with single defective coupling.
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