We will discuss methods of circumventing the fermion doubling problem in 3+1d Hamiltonian lattice models. In particular, we will construct a 3+1d model with a single Weyl fermion and an exact UV symmetry which implies the conservation of chiral charge in the IR. We will do the same for the SU(2) symmetry of a single Weyl doublet, finding a connection between an object in integrability known as the Onsager algebra, and Witten's SU(2) anomaly. Time permitting, we will also discuss 2+1d models with the parity anomaly.

This talk is based on https://arxiv.org/abs/2503.07708 with Lei Gioia (Caltech)

(online talk)