Wave function multifractality and dephasing at metal–insulator and quantum Hall transitions |
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Authors: | I.S. Burmistrov S. Bera F. Evers I.V. Gornyi A.D. Mirlin |
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Affiliation: | aL.D. Landau Institute for Theoretical Physics, Kosygina Street 2, 117940 Moscow, Russia;bDepartment of Theoretical Physics, Moscow Institute of Physics and Technology, 141700 Moscow, Russia;cInstitut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany;dInstitut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany;eA.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia;fPetersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia |
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Abstract: | We analyze the critical behavior of the dephasing rate induced by short-range electron–electron interaction near an Anderson transition of metal–insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in 2 + ? dimensions) with numerical simulations on the Chalker–Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data. |
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Keywords: | Anderson transitions Quantum Hall effect Dephasing Multifractality |
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