Multifractality at Anderson Transitions with Coulomb Interaction

Burmistrov, I. S.; Gornyi, I. V.; Mirlin, A. D.

doi:10.1103/physrevlett.111.066601

Cited by 55 publications

(79 citation statements)

References 48 publications

(50 reference statements)

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“…Recently, this conclusion was supported by numerical analysis in the framework of the density functional theory [30], by the Hartree-Fock simulation of the problem [31], and by the authors within the nonlinear sigma model analysis in d = 2 + ǫ dimension in the case of broken time reversal and spin rotational symmetries [32].…”

Section: Introductionmentioning

confidence: 85%

Multifractality and electron-electron interaction at Anderson transitions

2015

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Mesoscopic fluctuations and correlations of the local density of states are studied near metalinsulator transitions in disordered interacting electronic systems. We show that the multifractal behavior of the local density of states survives in the presence of Coulomb interaction. We calculate the spectrum of multifractal exponents in 2 + ǫ spatial dimensions for symmetry classes characterized by broken (partially or fully) spin-rotation invariance and show that it differs from that in the absence of interaction. We also estimate the multifractal exponents at the Anderson metal-insulator transition in 2D systems with preserved spin-rotation invariance. Our results for multifractal correlations of the local density of states are in qualitative agreement with recent experimental findings.

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Section: Introductionmentioning

confidence: 85%

Multifractality and electron-electron interaction at Anderson transitions

2015

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“…This method has previously been successfully applied to the Anderson transition 12,13 . In addition, two recent papers 25,26 have shown that multi-fractality survives in the presence of the Coulomb interaction.…”

Section: Multi-fractal Finite Size Scaling Analysismentioning

confidence: 99%

Critical exponent of metal-insulator transition in doped semiconductors: The relevance of the Coulomb interaction

Harashima

Slevin

2014

Phys. Rev. B

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We report a simulation of the metal-insulator transition in a model of a doped semiconductor that treats disorder and interactions on an equal footing. The model is analysed using density functional theory. From a multi-fractal analysis of the Kohn-Sham eigenfunctions, we find ν ≈ 1.3 for the critical exponent of the correlation length. This differs from that of Anderson's model of localisation and suggests that the Coulomb interaction changes the universality class of the transition.

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“…Attempts to address this question have been performed in numerical analysis of disordered electrons with Coulomb interaction in the framework of functional density theory [28,29] and by numerical implementation of the Hartree-Fock scheme [30]. Recently, the detailed theory of mesoscopic fluctuations of the local density of states has been developed by the present authors within nonlinear sigma model treatment of disordered interacting electrons in d = 2 + dimensions [31][32][33]. It was demonstrated that moments of the local density of states at Mott-Anderson transitions behave generically similar to Eq.…”

Section: Pacsmentioning

confidence: 99%

“…In Refs. [31] it was shown that the q-th moment of the local density of states at E = T = 0 obeys the following scaling law:…”

Section: Pacsmentioning

confidence: 99%

Mesoscopic fluctuations of the local density of states in interacting electron systems

2017

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We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron-electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to Anderson-Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron-electron attraction. In both cases strong mesoscopic fluctuations of the local density of states exist. PACS:Introduction. -Since the seminal paper by P.W. Anderson [1] a study of the localization-delocalization quantum phase transition in noninteracting disordered systems has turned into a vast field of research (see Refs. [2, 3] for a review). As any other quantum phase transitions, Anderson transition is characterized by a set of critical exponents which controls the scaling of a divergent correlation length and different physical observables. However, contrary to ordinary quantum phase transitions, for an Anderson transition there is the additional set of critical exponents ∆

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Multifractality at Anderson Transitions with Coulomb Interaction

Cited by 55 publications

References 48 publications

Multifractality and electron-electron interaction at Anderson transitions

Multifractality and electron-electron interaction at Anderson transitions

Critical exponent of metal-insulator transition in doped semiconductors: The relevance of the Coulomb interaction

Mesoscopic fluctuations of the local density of states in interacting electron systems

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