Anomaly of conserved and nonconserved axial charges in Hamiltonian lattice gauge theory

We investigate the axial anomaly in Hamiltonian lattice gauge theory. The definition of axial charge operators is ambiguous, especially between conserved and nonconserved axial charges. While these charges appear to differ only by a higher-order term in lattice spacing, they do not coincide in the continuum limit. We demonstrate, through analytical and numerical calculations in 1+1 dimensions, that the conserved axial charge correctly reproduces the axial anomaly relation in continuous spacetime. Our finding would serve as a valuable lesson about doubler artifact in Hamiltonian time evolution of lattice gauge theory.