Title: RKKY Interactions and Multipole Order in Ab initio Wannier Model of CeCoSi

Abstract: We calculate the RKKY interactions derived from ab initio calculations for the intermetallic compound CeCoSi exhibiting the hidden nonmagnetic order at $T_0$ and examine the instability towards possible multipole orders within the random phase approximation. All 36 multipole interactions up to rank 5 are investigated, and the maximum susceptibility exhibits an antiferro order with $\boldsymbol{q}=\boldsymbol{0}$ for nonmagnetic multipoles of monopole $I$ and hexadecapole $H_{0}$, yielding a charge imbalance of $f$ electrons at two Ce atoms in the unit cell. The obtained order can explain some experiments.