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Magnetic and multipolar ordering in f electron systems takes place at lowtemperatures of order 1-10 Kelvin. Combinations of first-principles withmany-body calculations for such low-energy properties of correlated materialsare challenging problems. We address multipolar ordering in f electron systemsbased on the dynamical mean-field theory (DMFT) combined with densityfunctional theory. We derive the momentum-dependent multipolar susceptibilitiesand interactions by solving the Bethe-Salpeter (BS) equation of thetwo-particle Green's function. We apply the formalism to the prototypicalexample of multipolar ordering CeB6, and demonstrate that the experimentalquadrupole transition is correctly reproduced. This first-principles formalismbased on DMFT and BS equation has applications which are beyond the reach ofthe traditional RKKY formula. In particular, more itinerant electron systemsincluding 5f, 4d and 5d electrons can be addressed.

Multipolar ordering from dynamical mean field theory with application to CeB6