Metal-insulator transitions and transitions between different quantum Hall liquids are used to describe the physical ideas forming the basis of quantum phase transitions and the methods of application of theoretical results in processing experimental data. The following two theoretical schemes are discussed and compared: the general theory of quantum phase transitions, which has been developed according to the theory of thermodynamic phase transitions and relies on the concept of a partition function, and a theory that is based on a scaling hypothesis and the renormalization-group concept borrowed from quantum electrodynamics, with the results formulated in terms of flow diagrams.

PACS: 71.30.+h, 72.15.Rn, 73.43.Nq (all) DOI: 10.1070/PU2008v051n01ABEH006471 URL: https://ufn.ru/en/articles/2008/1/b/ 000256193500002 2-s2.0-43949147246 Citation: Gantmakher V F, Dolgopolov V T "Localized-delocalized electron quantum phase transitions" Phys. Usp. 51 3–22 (2008) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Гантмахер В Ф, Долгополов В Т «Квантовые фазовые переходы „локализованные-делокализованные электроны“» УФН 178 3–24 (2008); DOI: 10.3367/UFNr.0178.200801a.0003