Emergent Rank-5 ``Nematic'' Order in URu2Si2

In the strongly correlated $f$-electron systems, novel electronic states often appear due to the interplay between electron correlations and entangled spin and orbital degrees of freedom. A spectacular example is the so-called ``hidden-order'' phase in the heavy-electron metal URu$_{2}$Si$_{2}$. The phase transition is characterized by the large amount of entropy loss observed at $T_{HO}=17.5$K, however no evidence of magnetic/structural phase transition below $T_{HO}$ have been reported so far. Despite efforts over a quarter century, the order parameter has remained unidentified. We show here that the hidden order is a rank-5 multipole (dotriacontapole) state with $E^{-}$ symmetry, based on the first-principles theoretical approach. This novel electronic state provides natural explanations of the key features including anisotropic magnetic excitations, nearly degenerate antiferromagnetic state, and spontaneous fourfold symmetry breaking.