Hamiltonian Truncation of Large $N_f$ QED and Large $N$ Vector-like Theories in $d=2+1$

We consider a general class of large $N$ vector-like theories in $d=2+1$ in a Hamiltonian approach. We show that by using lightcone quantization and the $N\to \mathrm{\infty }$ limit, we can diagonalize the Hamiltonian exactly and construct the eigenstates, spectral density, S-matrix, and form factors for the theory. For concreteness, we mainly focus on QED${}_3$ at large $N_f$ as an explicit example. We comment on extending the approach to finite $N$ calculations.