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We construct a class of matrix models, where supersymmetry (SUSY) isspontaneously broken at the matrix size $N$ infinite. The models are obtainedby dimensional reduction of matrix-valued SUSY quantum mechanics. The potentialof the models is slowly varying, and the large-$N$ limit is taken with theslowly varying limit.  First, we explain our formalism, introducing an external field to detectspontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking.It is observed that SUSY is possibly broken even in systems in less thanone-dimension, for example, discretized quantum mechanics with a finite numberof discretized time steps. Then, we consider spontaneous SUSY breaking in theSUSY matrix models with slowly varying potential, where the external field isturned off after the large-$N$ and slowly varying limit, analogously to thethermodynamic limit in statistical systems. On the other hand, without takingthe slowly varying limit, in the SUSY matrix model with a double-well potentialwhose SUSY is broken due to instantons for finite $N$, a number ofsupersymmetric behavior is explicitly seen at large $N$. It convinces us thatthe instanton effect disappears and the SUSY gets restored in the large-$N$limit.

Spontaneous supersymmetry breaking in large-$N$ matrix models with slowly varying potential