A two-dimensional realization of the parity anomaly

TL;DR

This paper demonstrates the realization of the parity anomaly in a synthetic two-dimensional ultracold atom system, revealing a half-quantized Hall response at a topological phase transition, thus providing a new platform to study quantum anomalies.

Contribution

It reports the first observation of a parity-anomalous Hall response in a genuinely two-dimensional synthetic quantum system, linking topology, symmetry, and quantum anomalies.

Findings

Observation of a half-quantized Hall drift at the Dirac point.

Protection of the response by an emergent parity symmetry.

Disappearance of the response when parity symmetry is broken.

Abstract

Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response. Anomaly inflow mechanism allows this effect to be observed at the surfaces of three-dimensional topological insulators, however, its realization in a genuinely two-dimensional system has remained elusive. Here we report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall topological phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms. By coupling a continuous spatial dimension to a finite synthetic dimension encoded in atomic spin states, we engineer tunable Chern bands with C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we observe a robust half-quantized Hall drift despite strong non-adiabatic excitations. We show that this response originates from the global structure of the band topology, is protected by an emergent parity symmetry at criticality, and disappears when parity is explicitly broken. Our work establishes synthetic quantum systems as a powerful platform to probe quantum anomalies and their interplay with topology and non-equilibrium dynamics.