Parity Anomaly at a Quantum Hall Critical Point in a Synthetic Two-Dimensional Lattice

Quantum anomalies arise when symmetries of a classical theory are broken by quantum fluctuations, leading to unconventional topological responses. A paradigmatic example is the parity anomaly of a two-dimensional Dirac fermion, which produces a half-quantised Hall conductance. While this effect is well known at magnetically gapped surfaces of three-dimensional topological insulators, its realisation in a genuinely two-dimensional system has remained elusive.

Here we report the experimental observation of a parity-anomalous Hall response in a synthetic two-dimensional system of ultracold dysprosium atoms. Using the atomic spin J=8 as a synthetic dimension coupled to one real spatial dimension, we engineer effective two-dimensional band structures with tunable Chern numbers C=0 and C=1. By tuning the system to the critical point of a quantum Hall topological phase transition, the bulk gap closes at a single Dirac point. At this point, we directly measure a half-quantised Hall conductance. We further demonstrate that the observed response is robust against perturbations that preserve the emergent parity symmetry of the low-energy Dirac Hamiltonian, while generic parity-breaking terms destroy the half-quantisation. These results establish a controllable cold-atom platform for studying quantum anomalies and show how half-quantised topological responses can emerge dynamically at a fine-tuned critical point in a truly two-dimensional quantum system.