This review explores the emergent phenomena in condensed matter physics, focusing on significant advancements from 2012 to 2021. It examines the theoretical foundations, including mean field theory and renormalization group theory, and delves into quantum phenomena such as quantum phase transitions and topological insulators. The review highlights developments in strongly correlated systems, particularly high-temperature superconductivity and quantum spin liquids, and discusses the unique properties and applications of low-dimensional systems like graphene and nanostructures. Additionally, it covers emergent phenomena in magnetism, including spintronics and skyrmions, and summarizes key experimental techniques like scanning tunneling microscopy and angle-resolved photoemission spectroscopy. The technological innovations and future prospects in electronics and energy storage are also addressed, underscoring the profound impact of emergent phenomena on both fundamental research and practical applications.

Emergent phenomena, condensed matter physics, quantum phase transitions, topological insulators, high-temperature superconductivity, quantum spin liquids, graphene, nanostructures, spintronics, skyrmions, scanning tunneling microscopy, angle-resolved photoemission spectroscopy.