  We develop the theory of Hamiltonian Truncation (HT) to systematically study
RG flows that require the renormalization of coupling constants. This is a
necessary step towards making HT a fully general method for QFT calculations.
We apply this theory to a number of QFTs defined as relevant deformations of
$d=1+1$ CFTs. We investigated three examples of increasing complexity: the
deformed Ising, Tricritical-Ising, and non-unitary minimal model $M(3,7)$. The
first two examples provide a crosscheck of our methodologies against well
established characteristics of these theories. The $M(3,7)$ CFT deformed by its
$Z_2$-even operators shows an intricate phase diagram that we clarify. At a
boundary of this phase diagram we show that this theory flows, in the IR, to
the $M(3,5)$ CFT.
