Experimental observation of exact quantum critical states

Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical, with the third one exhibiting the exotic properties in-between the former two. Confirming the presence of critical states is challenging, as it typically necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple superconducting qubit quantum system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges.