![]() Hermitian phase transitions ( a) are marked by gap closures along the real line. Being strongly affected by minute perturbations around the critical point, such behavior may prove useful in sensing applications 41, 42. complex spectrum or presence/absence of topological modes at different system sizes. Importantly, at experimentally accessible finite system sizes, the jump smooths out into an interpolation between the two phases in a strongly size-dependent manner, such that the system may exhibit qualitatively different properties, i.e., real vs. As elaborated below, this behavior appears generically whenever systems of dissimilar NHSE localization lengths are coupled, no matter how weakly. A CNHSE transition, by contrast, is characterized by a discontinuous jump between two different complex spectra along with two different sets of eigenstates. 1), where the eigenenergy spectrum can be continuously interpolated across the two bordering phases. This is distinct from previously known phase transitions (Hermitian and non-Hermitian) (Fig. We uncover here a class of criticality, dubbed the “critical non-Hermitian skin effect (CNHSE)”, where the eigenenergies and eigenstates in the thermodynamic limit “jump” between different skin solutions discontinuously across the critical point. Recently, concepts crucial to criticalities-like band gaps and localization-have been challenged by studies of non-Hermitian systems 15, 16 exhibiting exceptional points 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 or the non-Hermitian skin effect (NHSE), which are characterized by enigmatic bulk-boundary correspondence (BBC) violations, robust-directed amplifications, discontinuous Berry curvature, and anomalous transport behavior 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40. ![]() ![]() They have broad ramifications in conformal and statistical field theory 1, 2, 3, 4, Schramm–Loewner evolution 5, 6, entanglement entropy (EE) 7, 8, 9, 10, 11, 12, 13, 14, and many other contexts. Lying at the boundary between distinct phases, critical systems exhibit a wide range of interesting universal properties from divergent susceptibilities to anomalous scaling behavior. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics. More spectacularly, topological in-gap modes can even be induced by changing the system size. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. 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 critical scenarios with spectrum remaining continuous across a transition. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics.
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