Observation of quantum criticality of a four-dimensional phase transition

Understanding how a system’s behavior extrapolates beyond 3D is a fundamental question in physics, spanning topics from unification theories to critical phenomena. In statistical physics, fluctuations’ strength is highly sensitive to dimensionality, affecting phase transitions. In low dimensions, phase transitions are suppressed, while high-dimensional systems exhibit simpler mean-field behavior. In some cases, like the Anderson localization-delocalization transition in disordered media, criticality remains non-trivial even in dimensions larger than three, presenting challenges to existing frameworks. In this work, using a periodically-driven ultracold atomic gas to engineer disorder and synthetic dimensions, we experimentally observe a phase transition between localized and delocalized phases. The results display three key features of the 4D transition: 1) observables follow d=4 critical scale invariance, 2) critical exponents match numerical predictions for the 4D Anderson transition, and 3) they agree with Wegner’s relation in 4D. These findings provide a new avenue for exploring complex critical phenomena in higher dimensions.