Two-eigenfunction correlation in a multifractal metal and insulator

Cuevas, E.; Kravtsov, V. E.

doi:10.1103/physrevb.76.235119

Cited by 102 publications

(204 citation statements)

References 28 publications

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“…One can see a large enhancement of the correlation at small ω, and decreasing behavior with growing energy separations, which is similar to the results of Ref. 34 for the orthogonal Anderson model. Examining the same correlation for critical eigenfunctions in QCD, we also find an enhancement at small energy separations, see Fig.…”

Section: Correlations Between Eigenvectorssupporting

confidence: 88%

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

et al. 2015

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We investigate the Anderson transition found in the spectrum of the Dirac operator of Quantum Chromodynamics (QCD) at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determine the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high-temperature, and further support that it belongs to the 3D unitary Anderson model class.

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Section: Correlations Between Eigenvectorssupporting

confidence: 88%

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

et al. 2015

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“…They lead to the local suppression of wave function amplitudes at random locations [14]. Multifractal states are power-law correlated over a large energy interval E c of the order of the band width D [15,16]. We show that these spectral correlations induce local pseudogaps which, in turn, prevent the Kondo screening of a sizeable fraction of local…”

mentioning

confidence: 85%

“…Correlations between wave functions at different energies can then open wide local pseudogaps. These correlations can be quantified by spatially integrating the correlation function of eigenfunction probabilities associated with two energy levels distant in energy by ω nm = E n − E m , namely [16],…”

mentioning

confidence: 99%

Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities

2009

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It is well-known that magnetic impurities can change the symmetry class of disordered metallic systems by breaking spin and time-reversal symmetry. At low temperature these symmetries can be restored by Kondo screening. It is also known that at the Anderson metal-insulator transition, wave functions develop multifractal fluctuations with power law correlations. Here, we consider the interplay of these two effects. We show that multifractal correlations open local pseudogaps at the Fermi energy at some random positions in space. When dilute magnetic impurities are at these locations, Kondo screening is strongly suppressed. We find that when the exchange coupling J is smaller than a certain value J * , the metal-insulator transition point extends to a critical region in the disorder strength parameter and to a band of critical states. The width of this critical region increases with a power of the concentration of magnetic impurities.Fifty years after its proposal, the Anderson metal-insulator transition (AMIT) of disordered noninteracting electrons [1] continues to be intensively studied [2,3,4,5]. The AMIT is a quantum phase transition of second order where the localization length diverges with a critical exponent ν. The critical state is multifractal and characterized by a wide distribution of wave function amplitudes with a log-normal shape [5]. One aspect which remains less understood is the interplay between the AMIT of conduction electrons and the dynamics of the spin of magnetic impurities. These can be induced by energy levels below the Fermi energy such as the d-levels of transition metal impurities [6] or by localized electronic states such as the dopant levels in semiconductors [7]. Magnetic moments can enhance the spin susceptibility and the specific heat as has been observed in Si:P close to the AMIT [8,9]. When local magnetic moments interact with the conduction electrons by an exchange interaction, they can break both spin degeneracy and time-reversal symmetry (TRS) of the conduction electrons. Therefore, they are expected to change the symmetry class of the electronic system from orthogonal to unitary [10], changing the critical exponent ν, the critical electron density n c , and the critical disorder strength W c at which the transition occurs [11,12]. At sufficiently low temperatures, an additional effect comes into play. The antiferromagnetic exchange interaction between spin-1/2 local moments and the conduction electrons in a metal leads to a correlated electron state where a Kondo singlet is formed, screening the local moments at temperatures below the Kondo temperature T K . In this limit, the magnetic susceptibility χ approaches a constant value, as indicated in the left inset of Fig. 1, and the magnetic moments cease to break the TRS of the conduction electrons. The situation is quite different in the insulating phase, where local spectral gaps ∆ I prevent the development of the Kondo screening whenever the exchange coupling J between local moments and conduction electrons is below a criti...

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“…We also derive the general properties of RSB solutions that follow from this symmetry and do not rely on the particular approximation such as (38). Our first goal is to prove that for long paths ( 1) the distribution function of the product…”

Section: Appendix C: Termination Point Of Rsb Solutionmentioning

confidence: 99%

Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph

2018

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We develop a novel analytical approach to the problem of single particle localization in infinite dimensional spaces such as Bethe lattice and random regular graph models. The key ingredient of the approach is the notion of the inverted order thermodynamic limit (IOTL) in which the coupling to the environment goes to zero before the system size goes to infinity. Using IOTL and Replica Symmetry Breaking (RSB) formalism we derive analytical expressions for the fractal dimension D1 that distinguishes between the extended ergodic, D1 = 1, and extended non-ergodic (multifractal), 0 < D1 < 1 states on the Bethe lattice and random regular graphs with the branching number K. We also employ RSB formalism to derive the analytical expression ln Sfor the typical imaginary part of self-energy Styp in the non-ergodic phase close to the Anderson transition in the conventional thermodynamic limit. We prove the existence of an extended nonergodic phase in a broad range of disorder strength and energy and establish the phase diagrams of the models as a function of disorder and energy. The results of the analytical theory are compared with large-scale population dynamics and with the exact diagonalization of Anderson model on random regular graphs. We discuss the consequences of these results for the many body localization. Contents

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Two-eigenfunction correlation in a multifractal metal and insulator

Cited by 102 publications

References 28 publications

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

Critical Metal Phase at the Anderson Metal-Insulator Transition with Kondo Impurities

Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph

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