Entanglement asymmetry characterization of the Chiral Anomaly

Shao et al. recently showed that the 1+1D staggered fermion Hamiltonian admits a whole algebra of lattice operators that flow to the same axial charge in the thermodynamic limit (TL). On the lattice the principal axial charge does not commute with the vector charge, although their commutator is expected to vanish in the TL, providing a lattice realization of the chiral anomaly. We investigate the effect of this anomaly on the ground state(s) using the entanglement asymmetry. Unexpectedly, the asymmetry remains nonzero in the TL, despite the vanishing of the commutator, and exhibits a novel scaling behavior.