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By generalizing the Landau-Ginzburg/Calabi-Yau correspondence forhypersurfaces, we can relate a Calabi-Yau complete intersection to a hybridLandau-Ginzburg model: a family of isolated singularities fibered over aprojective line. In recent years Fan, Jarvis, and Ruan have defined quantuminvariants for singularities of this type, and Clader and Clader-Ross haveprovided a equivalence between these invariants and Gromov-Witten invariants ofcomplete intersections. For Calabi-Yau complete intersections of two cubics, weshow that this equivalence is directly related - via Chen character - to theequivalences between the derived category of coherent sheaves and that ofmatrix factorizations of the singularities. This generalizesChiodo-Iritani-Ruan's theorem matching Orlov's equivalences and quantum LG/CYcorrespondence for hypersurfaces.

Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations