This book comprehensively presents an unconventional quantum criticality caused by valence fluctuations, which offers theoretical understanding of unconventional Fermi-liquid properties in cerium- and ytterbium-based heavy fermion metals including CeCu₂(Si, Ge)₂ and CeRhIn₅ under pressure, and quasicrystal β-YbAlB₄ and Yb₁₅Al₃₄Au₅₁.

The book begins with an introduction to fundamental concepts for heavy fermion systems, valence fluctuation, and quantum phase transition, including self-consistent renormalization group theory. A subsequent chapter is devoted to a comprehensive description of the theory of the unconventional quantum criticality based on a valence transition, featuring explicit temperature dependence of various physical quantities, which allows for comparisons to relevant experiments. Lastly, it discusses how ubiquitous the valence fluctuation is, presenting candidate materials not only in heavy fermions, but also in strongly correlated electrons represented by high-T_c superconductor cuprates.

Introductory chapters provide useful materials for learning fundamentals of heavy fermion systems and their theory. Further, experimental topics relevant to valence fluctuations are valuable resources for those who are new to the field to easily catch up with experimental background and facts.

Shinji Watanabe is a professor in the Department of Basic Sciences at the Kyushu Institute of Technology. He received his Doctor of Science from Tohoku University in 2000. He was a post-doctoral research fellow at Osaka University, a research associate at the Institute for Solid-State Physics (ISSP) of The University of Tokyo and at the School of Engineering of The University of Tokyo, and an associate professor in the Department of Materials Physics at Osaka University and in the Department of Basic Sciences at the Kyushu Institute of Technology. He has served in his current position since 2021. His work is concerned with strongly correlated electrons and quantum many-body problems.

Kazumasa Miyake is an invited professor in the Graduate School of Science at Osaka University. He received his Doctor of Science from Nagoya University in 1979. He was an assistant and associate professor at Nagoya University in 1976-1987 and 1987-1991, respectively, and an associate professor and professor at Osaka University in 1991-1994 and 1994-2013, respectively. After his retirement in 2013, he was a fellow at the Toyota Physical and Chemical Research Institute until 2017 and has been an invited professor at Osaka University since 2017. His work is concerned with condensed matter theory, particularly superconductivity and magnetism in strongly correlated electrons.