Terminal-coupling induced critical eigenspectrum transition in closed non-Hermitian loops

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Topological Physics

Background:

• Non-Hermitian (NH) systems exhibit the non-Hermitian skin effect (NHSE), causing distinct eigenenergy spectra under open boundary conditions (OBC) and periodic boundary conditions (PBC).
• Critical NHSE typically requires multiple coupled NH chains, where inter-chain coupling significantly alters the spectrum compared to individual chains.

Purpose of the Study:

• To demonstrate that critical NHSE can be induced in a single finite-length non-Hermitian chain with a closed-loop configuration.
• To challenge the conventional understanding that multiple chains are necessary for critical NHSE transitions.

Main Methods:

• Investigating a single finite-length non-Hermitian chain with weak terminal coupling forming a closed loop.
• Analytical explanation of the effect using a Hatano-Nelson chain model.
• Demonstrating the generality of the phenomenon in various one-dimensional NH chains.

Main Results:

• An infinitesimally small terminal coupling can cause an abrupt switch between OBC and PBC spectra in the closed-loop system.
• This spectral switch is critically dependent on the chain length exceeding a specific size limit.
• The critical effect arises from the interplay of boundary conditions and edge localization.

Conclusions:

• Critical NHSE is not exclusive to multi-chain systems and can be realized in a single closed-loop NH chain.
• Finite-size effects and boundary conditions play a crucial role in inducing critical phenomena in NH systems.
• The findings highlight the generality of critical size-dependent effects in finite NH systems.