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We propose a generalization of the Grover-Sheng-Vishwanath model which, assolved by the density-matrix renormalization group, realizes the emergentsupersymmetric criticality in the universality class of the even series of the$\mathcal{N}\!=\!1$ superconformal minimal models characterized by a centralcharge $5/4$. This chain model describes the topological phase transition ofthe propagating Majorana edge mode in topological superconductors coupled withthe two-flavour Ising magnetic fluctuations (or the $XZ$ type). Usingbosonization and perturbative renormalization group, we show that the augmenteddegrees of freedom trigger a paradigm shift from the supersymmetricLandau-Ginzburg action to the variant of the supersymmetric sine-Gordonequation, which, in the massless case, can flow towards the supersymmetricminimal series upon a generalized Feigin-Fuchs construction. Therefore, thepresent lattice model comprises a concrete system that exhibits the spacetimesupersymmetry through the distinct route.

From supersymmetric sine-Gordon equation to the superconformal minimal model