Experimental observation of parity anomaly in a synthetic two-dimensional quantum system

Quantum anomalies reflect the breakdown of classical symmetries by quantum fluctuations and give rise to unconventional topological responses. A paradigmatic example is the parity anomaly of a two-dimensional Dirac fermion, where lattice regularisation prevents global parity conservation and leads to a half-quantised Hall conductance. While this effect appears at magnetically gapped surfaces of three-dimensional topological insulators, its realisation in a genuinely two-dimensional system remains challenging. Here, we experimentally observe a parity-anomalous Hall response in a synthetic two-dimensional system of ultracold dysprosium atoms tuned to the critical point of a quantum Hall topological phase transition. By coupling the atomic spin J = 8 as a synthetic dimension to one spatial dimension, we engineer effective two-dimensional bands with tunable Chern numbers C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we measure a half-quantised Hall conductance. We show that this response is robust against perturbations preserving the emergent parity symmetry of the low-energy Dirac Hamiltonian, but is destroyed by generic parity-breaking terms. Our results demonstrate how half-quantised topological responses can emerge dynamically at a fine-tuned critical point in a truly two-dimensional quantum system.