Speaker
Description
We investigate the mass term structure and anomalies of the 3+1-dimensional staggered fermion Hamiltonian. We show that the lattice Hamiltonian possesses conserved charges generating the Onsager algebra, which realize $\mathrm{U}(1)_{F_i} \subset \mathrm{SU}(2)_L \times \mathrm{SU}(2)_R$ $(i = x, y, z)$ in the continuum limit. We classify all bilinear mass terms local within a unit cube and clarify the symmetries preserved by each, showing that no mixed 't Hooft anomaly exists between $\mathrm{U}(1)_V$ and $\mathrm{U}(1)_{F_i}$. We further show that introducing a kink profile of the $x$-direction one-link mass --- which preserves the largest residual symmetry among all mass terms --- gaps the 3+1D bulk and localizes two-flavor massless Dirac fermions on the 2+1D domain wall. The bulk Onsager-algebra charges act on the wall as generators of a flavor $\mathrm{SU}(2)$ symmetry, whose associated parity anomaly forbids any symmetric mass gap on the boundary. This shows that the boundary flavor symmetry and its anomaly are not emergent but descend from the ultraviolet lattice Hamiltonian.