Staggered Fermions with Chiral Anomaly Cancellation

We investigate the implications of the quantized vectorial and axial charges in the lattice Hamiltonian of multi-flavor staggered fermions in $(1+1)$ dimensions. These lattice charges coincide with those of the $U(1)_V$ and $U(1)_A$ global symmetries of Dirac fermions in the continuum limit, whose perturbative chiral anomaly matches the non-Abelian Onsager algebra on the lattice. In this note, we focus on the lattice models that flow to continuum quantum field theories of Dirac fermions that are free from the perturbative chiral anomaly between $U(1)_V$ and $U(1)_A$. In a lattice model that flows to two Dirac fermions, we identify quadratic Hamiltonian deformations that can gap the system while fully preserving both the vectorial and axial charges on the lattice. These deformations flow to the usual symmetry-preserving Dirac mass terms in the continuum. Additionally, we propose a lattice model that flows to the chiral fermion $3-4-5-0$ model in the continuum by using these lattice charges, and we discuss the multi-fermion interactions that can generate a mass gap in the paradigm of symmetric mass generation.