Critical non-Hermitian Skin Effect

Understand

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.