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) ↓

A.A. Shashkin “Metal-insulator transitions and the effects of electron-electron interactions in two-dimensional electron systems” 48 129–149 (2005)
S.M. Stishov “Quantum phase transitions” 47 789–795 (2004)
V.F. Gantmakher, V.T. Dolgopolov “Superconductor-insulator quantum phase transition” 53 1–49 (2010)
V.T. Dolgopolov “Two-dimensional system of strongly interacting electrons in silicon (100) structures” 62 633–648 (2019)
E.L. Shangina, V.T. Dolgopolov “Quantum phase transitions in two-dimensional systems” 46 777–787 (2003)
V.T. Dolgopolov “Integer quantum Hall effect and related phenomena” 57 105–127 (2014)
A.A. Likal’ter “Critical points of condensation in Coulomb systems” 43 777–797 (2000)
B.I. Shklovskii, A.L. Éfros “Percolation theory and conductivity of strongly inhomogeneous media” 18 845–862 (1975)
K.V. Reich “Conductivity of quantum dot arrays” 63 994–1014 (2020)
B.S. Dumesh “Influence of quantum fluctuations on the magnetic properties of quasi-one-dimensional triangular antiferromagnets” 43 365–380 (2000)
E.Z. Kuchinskii, I.A. Nekrasov, M.V. Sadovskii “Generalized dynamical mean-field theory in the physics of strongly correlated systems” 55 325–355 (2012)
M.V. Sadovskii “Pseudogap in high-temperature superconductors” 44 515–539 (2001)
B.I. Belevtsev “Superconductivity and localization of electrons in disordered two-dimensional metal systems” 33 (1) 36–54 (1990)
G.A. Martynov “The problem of phase transitions in statistical mechanics” 42 517–543 (1999)
Yu.A. Izyumov “Hubbard model of strong correlations” 38 385–408 (1995)
R.O. Zaitsev, E.V. Kuz’min, S.G. Ovchinnikov “Fundamental ideas on metal-dielectric transitions in 3d-metal compounds” 29 322–342 (1986)
B.V. Alekseev “Physical fundamentals of the generalized Boltzmann kinetic theory of ionized gases” 46 139–167 (2003)
Yu.A. Izyumov, E.Z. Kurmaev “Materials with strong electron correlations” 51 23–56 (2008)
N.B. Ivanova, S.G. Ovchinnikov et al “Specific features of spin, charge, and orbital ordering in cobaltites” 52 789–810 (2009)
E.G. Maksimov, Yu.I. Shilov “Hydrogen at high pressure” 42 1121–1138 (1999)

The list is formed automatically.