Localized – delocalized electron quantum phase transitions

V.F. Gantmakher, V.T. Dolgopolov
Osipyan Institute of Solid State Physics, Russian Academy of Sciences, Akademika Osip'yana str. 2, Chernogolovka, Moscow Region, 142432, Russian Federation

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/
Web of Science

000256193500002
Scopus

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

References (36) ↓ Cited by (49) Similar articles (20)

Sachdev S Quantum Phase Transitions (Cambridge: Cambridge Univ. Press, 1999)
Sondhi S L et al. "Continuous quantum phase transitions" Rev. Mod. Phys. 69 315 (1997)
Vojta T "Quantum phase transitions" In Computational Statistical Physics (Eds K H Hoffmann, M Schreiber) (Berlin: Springer, 2002); Vojta T cond-mat/0010285
Thouless D J Phys. Rep. 13 93 (1974)
Patashinskii A Z, Pokrovskii V L Fluktuatsionnaya Teoriya Fazovykh Perekhodov 2-e izd. (M.: Nauka, 1982); Translated into English, Patashinskii A Z, Pokrovskii V L Fluctuation Theory Of Phase Transitions (Oxford: Pergamon Press, 1979)
Goldenfeld N Lectures On Phase Transitions And The Renormalization Group (Reading, Mass.: Addison-Wesley, 1992)
Abrahams E et al. Phys. Rev. Lett. 42 673 (1979)
Fisher M E "Renormalization group theory: its basis and formulation in statistical physics" Rev. Mod. Phys. 70 653 (1998)
Lee P A, Ramakrishnan T V "Disordered electronic systems" Rev. Mod. Phys. 57 287 (1985)
Gantmakher V F Elektrony v Neuporyadochennykh Sredakh 2-e izd. (M.: Fizmatlit, 2005)
Altshuler B I, Aronov A G "Electron – electron interaction in disordered conductors" In Electron – Electron Interactions In Disordered Systems (Modern Problems in Condensed Matter Sciences, Vol. 10, Eds A L Efros, M Pollak) (Amsterdam: North-Holland, 1985)
Imry Y J. Appl. Phys. 52 1817 (1981)
Al’tshuler B L, Aronov A G Pis’ma ZhETF 37 349 (1983); Al’tshuler B L, Aronov A G JETP Lett. 37 410 (1983)
Dodson B W et al. Phys. Rev. Lett. 46 46 (1981)
Imry Y, Ovadyahu Z J. Phys. C 15 L327 (1982)
Maliepaard M C et al. Phys. Rev. Lett. 61 369 (1988)
Teplinskii V M, Gantmakher V F, Barkalov O I Zh. Eksp. Teor. Fiz. 101 1698 (1992); Teplinskii V M, Gantmakher V F, Barkalov O I Sov. Phys. JETP 74 905 (1992)
Shlimak I et al. Phys. Rev. Lett. 77 1103 (1996); Shlimak I et al. J. Phys. Condens. Matter 9 9873 (1997)
Castner T G "Hopping conduction in the critical regime approaching the metal – insulator transition" In Hopping Transport In Solids (Modern Problems in Condensed Matter Sciences, Vol. 28, Eds M Pollak, B Shklovskii) (Amsterdam: North-Holland, 1991)
Larkin A I, Khmel’nitskii D E Zh. Eksp. Teor. Fiz. 83 1140 (1982); Larkin A I, Khmel’nitskii D E Sov. Phys. JETP 56 647 (1982)
Dobrosavljević V et al. Phys. Rev. Lett. 79 455 (1997)
Bergmann G Phys. Rep. 107 1 (1984)
Hikami S, Larkin A I, Nagaoka Y Prog. Theor. Phys. 63 707 (1980)
McMillan W L Phys. Rev. B 24 2739 (1981)
Punnoose A, Finkel’stein A M Science 310 289 (2005)
Kravchenko S V et al. Phys. Rev. B 50 8039 (1994)
Anissimova S et al. Nature Phys. 3 707 (2007); Anissimova S et al. cond-mat/0609181
Gantmakher V F et al. Pis’ma ZhETF 71 231 (2000); Gantmakher V F JETP Lett. 71 160 (2000)
Ebert G et al. Solid State Commun. 44 95 (1982)
Khmel’nitskii D E Pis’ma ZhETF 38 454 (1983); Khmel’nitskii D E JETP Lett. 38 552 (1983)
Shashkin A A, Dolgopolov V T, Kravchenko G V Phys. Rev. B 49 14486 (1994)
Balaban N Q, Meirav U, Bar-Joseph I Phys. Rev. Lett. 81 4967 (1998)
Wanli Li et al. Phys. Rev. Lett. 94 206807 (2005)
Shashkin A A Usp. Fiz. Nauk 175 139 (2005); Shashkin A A Phys. Usp. 48 129 (2005)
Kivelson S, Lee D-H, Zhang S-C Phys. Rev. B 46 2223 (1992)
Huckestein B Rev. Mod. Phys. 67 357 (1995)