Critical non-Hermitian Skin Effect

• URL: http://arxiv.org/abs/2003.03039v1
• Date: Fri, 6 Mar 2020 05:48:46 GMT
• Title: Critical non-Hermitian Skin Effect
• Authors: Linhu Li, Ching Hua Lee, Sen Mu, and Jiangbin Gong
• Abstract summary: This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit. We present stimulating examples with anomalous scaling behavior regarding spectrum, correlation functions, entanglement entropy, and scale-free wavefunctions that decay exponentially rather than power-law.
• Score: 2.6109033135086777
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established Hermitian and non-Hermitian critical scenarios where spectrum remains continuous across a transition. Such critical behavior, dubbed the "critical skin effect", is rather generic, occuring whenever subsystems with dissimilar non-Hermitian skin localization lengths are coupled, however weakly. Due to the existence of this criticality, the thermodynamic limit and the zero-coupling limit cannot be exchanged, thus challenging the celebrated generalized Brillouin zone (GBZ) approach when applied to finite-size systems. As manifestations of the critical skin effect in finite-size systems, we present stimulating examples with anomalous scaling behavior regarding spectrum, correlation functions, entanglement entropy, and scale-free wavefunctions that decay exponentially rather than power-law. More spectacularly, topological in-gap modes can even be induced by changing the system size.

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