The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wave function itself remains only partially understood. In this work, we introduce a family of multipartite entanglement measures that probe chirality directly from the bulk wavefunction. Our construction involves applying different permutations between replicas of the ground-state wave function in neighboring spatial regions, creating “permutation defects” at the boundaries between these regions. We provide general arguments for the robustness of these measures and develop a field-theoretical framework to compute them systematically. While the standard topological field-theory prescription misses the chiral contribution, our method correctly identifies it as the chiral conformal field-theory partition function on high-genus Riemann surfaces. This feature is a consequence of the bulk-edge correspondence, which dictates that any regularization of the theory at the permutation defects must introduce gapless boundary modes. We numerically verify our results with both free-fermion and strongly interacting chiral topological states and find excellent agreement. Our results enable the extraction of the chiral central charge and the Hall conductance using a finite number of wave function replicas, making these quantities accessible to Monte Carlo numerical techniques and noisy intermediate-scale quantum devices.

Close

PrevNext

View figure in article

• Entanglement measures
• Quantum Hall effect
• Topological field theories
• Topological order
• Conformal field theory