Multipole fluctuation theory for heavy fermion systems: Application to multipole orders in CeB6

In heavy fermion systems, multipole degrees of freedom make possible the emergence of rich phenomena, such as hidden orders and superconductivities. However, many of them remain unsolved since the origin of higher-rank multipole interaction is not well understood. Among these issues, we focus on the quadrupole order in CeB$_6$, which is a famous multipolar heavy fermion system actively studied for decades. We analyze the multiorbital periodic Anderson model for CeB$_6$, and find that both magnetic, quadrupole, and octupole fluctuations develop cooperatively due to the strong inter-multipole coupling given by higher-order many-body effects, called the vertex corrections. It is found that the antiferro-quadrupole order in CeB$_6$ is driven by the interference between magnetic-multipole fluctuations. The discovered inter-multipole coupling mechanism is a potential origin of various hidden orders in various heavy fermion systems.