  We use Lightcone Conformal Truncation to analyze the RG flow of the
two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a
real scalar superfield with a $\mathbb{Z}_2$-symmetric cubic superpotential.
The theory depends on a single dimensionless coupling $\bar{g}$, and is
expected to have a critical point at a tuned value $\bar{g}_*$ where it flows
in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks
the $\mathbb{Z}_2$ symmetry on one side of this phase transition, and breaks
SUSY on the other side. We calculate the spectrum of energies as a function of
$\bar{g}$ and see the gap close as the critical point is approached, and
numerically read off the critical exponent $\nu$ in TIM. Beyond the critical
point, the gap remains nearly zero, in agreement with the expectation of a
massless Goldstino. We also study spectral functions of local operators on both
sides of the phase transition and compare to analytic predictions where
possible. In particular, we use the Zamolodchikov $C$-function to map the
entire phase diagram of the theory. Crucial to this analysis is the fact that
our truncation is able to preserve supersymmetry sufficiently to avoid any
additional fine tuning.
