Critical states are defined by simultaneous absence of exponential localization in position and momentum space, with the Liu-Xia condition made rigorous and exactly predictive through a Fourier exclusion principle.
Exploring the Many-Body Localization Transition in Two Dimensions
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Lyapunov Exponents as Duality-Invariant Signatures of Critical States
Critical states are defined by simultaneous absence of exponential localization in position and momentum space, with the Liu-Xia condition made rigorous and exactly predictive through a Fourier exclusion principle.