A strong spin-orbit interaction and Coulomb repulsion featuring
strongly correlated d- and f-electron systems lead to various
exotic phase transition including unconventional superconductivity
and magnetic multipole order. However, their microscopic origins
are long standing problem since they could not be explained based
on conventional Migdal-Eliashberg theorem. The book focuses on
many-body correlation effects beyond conventional theory for the d-
and f-electron systems, and theoretically demonstrates the
correlations to play significant roles in "mode-coupling" among
multiple quantum fluctuations, which is called U-VC here. The
following key findings are described in-depth: (i) spin triplet
superconductivity caused by U-VC, (ii) being more important U-VC in
f-electron systems due to magnetic multipole degrees of freedom
induced by a spin-orbit interaction, and (iii) s-wave
superconductivity stabilized cooperatively by antiferromagnetic
fluctuations and electron-phonon interaction contrary to
conventional understanding. The book provides meaningful step for
revealing essential roles of many-body effects behind long standing
problems in strongly correlated materials.
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