  We propose a novel procedure of assigning a pair of non-unitary topological
quantum field theories (TQFTs), TFT$_\pm [\mathcal{T}_{\rm rank \;0}]$, to a
(2+1)D interacting $\mathcal{N}=4$ superconformal field theory (SCFT)
$\mathcal{T}_{\rm rank \;0}$ of rank 0, i.e. having no Coulomb and Higgs
branches. The topological theories arise from particular degenerate limits of
the SCFT. Modular data of the non-unitary TQFTs are extracted from the
supersymmetric partition functions in the degenerate limits. As a non-trivial
dictionary, we propose that $F = \max_\alpha \left(- \log |S^{(+)}_{0\alpha}|
\right) = \max_\alpha \left(- \log |S^{(-)}_{0\alpha}|\right)$, where $F$ is
the round three-sphere free energy of $\mathcal{T}_{\rm rank \;0 }$ and
$S^{(\pm)}_{0\alpha}$ is the first column in the modular S-matrix of TFT$_\pm$.
From the dictionary, we derive the lower bound on $F$, $F \geq -\log
\left(\sqrt{\frac{5-\sqrt{5}}{10}} \right) \simeq 0.642965$, which holds for
any rank 0 SCFT. The bound is saturated by the minimal $\mathcal{N}=4$ SCFT
proposed by Gang-Yamazaki, whose associated topological theories are both the
Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs)
correspondence for infinitely many examples.
