Multifractality and electron-electron interaction at Anderson transitions

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

doi:10.1103/physrevb.91.085427

Cited by 24 publications

(45 citation statements)

References 64 publications

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“…Upon resummation, they are expected to restore the divergence of γ c at a scale L c slightly larger than L X . At the same time, since the second-loop (k = 2) terms are similar to those describing the mesoscopic fluctuations of the superconducting order parameter [44,45], we expect for |γ c |t > 1 (i.e., for temperatures slightly above the transition) strong spatial fluctuations of the observables (in particular, of the local tunneling density of states [45,46], as observed in experiments, see, e.g., Ref. [11]).…”

Section: A Preserved Spin-rotational Symmetrysupporting

confidence: 64%

Superconductor-insulator transitions: Phase diagram and magnetoresistance

2015

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The influence of the disorder-induced Anderson localization and electron-electron interaction on the superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature T c , the temperature dependence of the resistivity, the phase diagram, and the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. The derived RG equations are valid to the lowest order in disorder but for an arbitrary electron-electron interaction strength in a particle-hole and the Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, with both short-range and long-range (Coulomb) interactions. In the case of short-range interaction, we identify parameter regions where the superconductivity is enhanced by localization effects. Our RG analysis indicates that the superconductor-insulator transition is controlled by a fixed point with a resistivity R c of the order of the quantum resistance R q = h/4e 2 . When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below T c .

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Section: A Preserved Spin-rotational Symmetrysupporting

confidence: 64%

Superconductor-insulator transitions: Phase diagram and magnetoresistance

2015

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“…-The anomalous dimension that governs the scaling behaviour of moments of the local density of states can be computed near two dimensions as a perturbative expansion in the dimensionless resistance t. In the most general case when both time reversal and spin rotational symmetries are preserved we obtained the following result [33]:…”

Section: Pacsmentioning

confidence: 74%

“…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%

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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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“…It was recently shown that multifractality at the Anderson transition remains in the presence of Coulomb interactions [6,7]. Multifractality also seems to play a prominent role in many-body systems subject to strong disorder [8,9], in which an insulating ("many-body localised") phase can emerge, corresponding to a many-particle wave function which is localised in Fock space [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Multifractality in Fock Space of the Ground State of the Bose-Hubbard Hamiltonian

Lindinger

Rodríguez

2017

Acta Phys. Pol. A

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We present a first study of the multifractal properties of the ground state of the Bose-Hubbard Hamiltonian in Fock space. Numerical simulations of system sizes up to L = 10 at unit filling suggest that multifractality is present for all values of the bosonic interaction strength. Moreover, the analysis of the generalised fractal dimensions for different densities exposes qualitatively the superfluid to Mott insulator phase transition.

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Multifractality and electron-electron interaction at Anderson transitions

Cited by 24 publications

References 64 publications

Superconductor-insulator transitions: Phase diagram and magnetoresistance

Superconductor-insulator transitions: Phase diagram and magnetoresistance

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

Multifractality in Fock Space of the Ground State of the Bose-Hubbard Hamiltonian

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