  By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for
hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid
Landau-Ginzburg model: a family of isolated singularities fibered over a
projective line. In recent years Fan, Jarvis, and Ruan have defined quantum
invariants for singularities of this type, and Clader and Clader-Ross have
provided a equivalence between these invariants and Gromov-Witten invariants of
complete intersections. For Calabi-Yau complete intersections of two cubics, we
show that this equivalence is directly related - via Chen character - to the
equivalences between the derived category of coherent sheaves and that of
matrix factorizations of the singularities. This generalizes
Chiodo-Iritani-Ruan's theorem matching Orlov's equivalences and quantum LG/CY
correspondence for hypersurfaces.
