Exploring Hamiltonian Truncation in $\bf{d=2+1}$

We initiate the application of Hamiltonian truncation methods to solve strongly coupled QFTs in d=2+1. By analysing perturbation theory with a Hamiltonian truncation regulator, we pinpoint the challenges of such an approach and propose a way that these can be addressed. This enables us to formulate Hamiltonian Truncation theory for ϕ4 in d=2+1, and to study its spectrum at weak and strong coupling. The results obtained agree well with the predictions of a weak/strong self-duality possessed by the theory. The ϕ4 interaction is a strongly relevant UV divergent perturbation, and represents a case study of a more general scenario. Thus, the approach developed should be applicable to many other QFTs of interest.