- The paper introduces the critical non-Hermitian skin effect by revealing discontinuous eigenenergy and eigenstate transitions driven by infinitesimal interchain coupling.
- It employs a model of two coupled 1D Hatano-Nelson chains to demonstrate anomalous scaling in spectra, correlation functions, and entanglement entropy.
- The study challenges standard GBZ approaches and highlights potential applications in sensing and topological material design through sensitivity to system size.
Critical Non-Hermitian Skin Effect
The paper "Critical non-Hermitian Skin Effect" introduces an innovative critical phenomenon in non-Hermitian lattice systems, challenging established paradigms of phase transitions. The paper reveals a unique form of criticality where eigenenergies and eigenstates of non-Hermitian systems experience discontinuous transitions at a critical point, notably differing from traditional Hermitian transitions where the spectrum remains continuous. Termed the "critical skin effect" (CSE), this critical behavior presents itself when subsystems with distinct non-Hermitian skin localization lengths are weakly coupled.
Main Findings and Methodology
The research draws attention to the fact that due to the CSE, the interchangeability of the thermodynamic and zero-coupling limits is not feasible, thereby questioning the generalized Brillouin zone (GBZ) approach commonly used for finite-size non-Hermitian systems. The critical nature of the CSE is highlighted through examples showing anomalous scaling behaviors in spectrum, correlation functions, entanglement entropy, and scale-free wave functions that exhibit exponential rather than power-law decay. Notably, the paper shows that topological in-gap modes can be introduced simply by modifying the system size.
This paper provides substantial theoretical analysis by examining a model of two coupled non-Hermitian 1D Hatano-Nelson chains. It demonstrates that even an infinitesimal coupling between the chains—when their non-Hermitian skin effects differ—can lead to complex transformations in the spectrum, transitioning from real to complex eigenvalues as the system size increases. This complex interaction is rigorously validated, including non-perturbative effects where the critical coupling scales inversely with system size, symbolizing the ongoing influence of weak inter-subsystem interactions in large systems.
Implications and Future Directions
The practical implications of this paper are significant. The unique sensitivity of these systems to weak perturbations at the critical point suggests utility in advanced sensing applications, as subtle system parameter changes can yield observable effects. The introduced CSE also prompts further investigation into the fundamental nature of non-Hermitian systems, as it challenges and refines the GBZ framework for finite systems. Moreover, it enriches the landscape of topological materials science, providing a novel perspective on structure-driven emergent phenomena often observed in metamaterials.
On the theoretical side, this paper beckons further exploration of criticality, particularly in how new classes of phase transitions can be modeled and qualitatively characterized. Future research could explore not only physical implementations in settings like electronic circuits or cold atom systems but also investigate the deeper connections between non-Hermitian physics and other domains, such as quantum information, where phase transitions play a crucial role.
In conclusion, this paper on the critical non-Hermitian skin effect deepens our understanding of non-Hermitian dynamics and offers novel insights into system behaviors that occur at unexpected junctures of coupling and system size. It opens pathways for developing engineered systems which utilize its sensitivity and novel configurations, shaping prospects for non-Hermitian physics and its technological applications.