Physics of Quantum Phase Transitions - Topological Quantum Criticality, Quantum Multi-Criticality and Novel Quantum Phases

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Nature of novel quantum criticality including marginal quantum criticality and quantum multi-criticality characterized by topology changes as well as proximity effects of first-order transitions were clarified. It was revealed that the divergence of the fluctuations at zero wave number generated around the multi-critical points is the origin of several unprecedented non-Fermi liquid properties. Quantum phase transitions between zero-gap semiconductors and topological insulators are shown to have dual characters of spontaneous symmetry breaking and topology change and thus show novel criticality. We have elucidated the mechanism of high-temperature superconductivity generated by the marginal quantum criticality.