In heavy fermion systems, the emergence of rich phenomena, such as hidden orders and superconductivities, is made possible by multipole degrees of freedom. However, many of them remain unsolved since the origin of the higher-rank multipole interaction is not well understood. Among these issues, we focus on the quadrupole order in CeB₆, which is a famous multipolar heavy fermion system that has been actively studied for decades. We analyze the multiorbital periodic Anderson model for CeB₆, and find that magnetic, quadrupole, and octupole fluctuations all develop cooperatively due to the strong intermultipole coupling given by higher-order many-body effects, called vertex corrections. It is found that the antiferroquadrupole order in CeB₆ is driven by the interference between magnetic-multipole fluctuations. The discovered intermultipole coupling mechanism is a potential origin of numerous hidden orders in various heavy fermion systems.

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