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N=4 supersymmetric quantum mechanical model is formulated on the lattice. Twosupercharges, among four, are exactly conserved with the help of the cyclicLeibniz rule without spoiling the locality. In use of the cohomologicalargument, any possible local terms of the effective action are classified intotwo categories which we call type-I and type-II, analogous to the D- andF-terms in the supersymmetric field theories. We prove non-renormalizationtheorem on the type-II terms which include mass and interaction terms withkeeping a lattice constant finite, while type-I terms such as the kinetic termshave nontrivial quantum corrections.

Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule