Elmeleti Fizika Tanszek

Budapest, Hungary

Elmeleti Fizika Tanszek

Budapest, Hungary
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Kettemann S.,Jacobs University Bremen | Kettemann S.,Pohang University of Science and Technology | Mucciolo E.R.,University of Central Florida | Varga I.,Elmeleti Fizika Tanszek | Slevin K.,Osaka University
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical power-law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero-temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time-reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature TK is derived at the AMIT, in the metallic phase, and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field B and at finite temperature T. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as a function of temperature. We find a phase diagram with finite-temperature transitions among insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions. © 2012 American Physical Society.


Mendez-Bermudez J.A.,Autonomous University of Puebla | Gopar V.A.,University of Zaragoza | Varga I.,Elmeleti Fizika Tanszek | Varga I.,University of Marburg
Physical Review B - Condensed Matter and Materials Physics | Year: 2010

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the power-law banded random matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth crossover from localized to delocalized behavior in the average-scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying b (the effective bandwidth of the PBRM model) from small (b≪1) to large (b>1) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit b→∞. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with b∈ [0.2,0.4] reproduces well the scattering and transport properties of the 3D Anderson model. © 2010 The American Physical Society.


Mendez-Bermudez J.A.,Autonomous University of Puebla | Martinez-Mendoza A.J.,Autonomous University of Puebla | Gopar V.A.,University of Zaragoza | Varga I.,Elmeleti Fizika Tanszek
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2016

We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies ε of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large ε, P(ε)∼1/ε1+α with α(0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to α=1. First, we verify that the ensemble average -lnG is proportional to the length of the wire L for all values of α, providing the localization length ξ from -lnG=2L/ξ. Then, we show that the probability distribution function P(G) is fully determined by the exponent α and -lnG. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to Gβ, for G→0, with β≤α/2, in agreement with previous studies. © 2016 American Physical Society.


Mendez-Bermudez J.A.,Autonomous University of Puebla | Alcazar-Lopez A.,Autonomous University of Puebla | Martinez-Mendoza A.J.,Elmeleti Fizika Tanszek | Rodrigues F.A.,University of Sao Paulo | Peron T.K.D.,University of Sao Paulo
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

By the use of extensive numerical simulations, we show that the nearest-neighbor energy-level spacing distribution P(s) and the entropic eigenfunction localization length of the adjacency matrices of Erdos-Rényi (ER) fully random networks are universal for fixed average degree ξ≡αN (α and N being the average network connectivity and the network size, respectively). We also demonstrate that the Brody distribution characterizes well P(s) in the transition from α=0, when the vertices in the network are isolated, to α=1, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks. © 2015 American Physical Society.


PubMed | University of Zaragoza, Autonomous University of Puebla and Elmeleti Fizika Tanszek
Type: Journal Article | Journal: Physical review. E | Year: 2016

We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large , P()1/^{1+} with (0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to =1. First, we verify that the ensemble average -lnG is proportional to the length of the wire L for all values of , providing the localization length from -lnG=2L/. Then, we show that the probability distribution function P(G) is fully determined by the exponent and -lnG. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to G^{}, for G0, with /2, in agreement with previous studies.


Ujfalusi L.,Elmeleti Fizika Tanszek | Giordano M.,Hungarian Academy of Sciences | Pittler F.,MTA ELTE Lattice Gauge Theory Research Group | Kovacs T.G.,Hungarian Academy of Sciences | Varga I.,Elmeleti Fizika Tanszek
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2015

We investigate the Anderson transition found in the spectrum of the Dirac operator of quantum chromodynamics 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. © 2015 American Physical Society.


Ujfalusi L.,Elmeleti Fizika Tanszek | Varga I.,Elmeleti Fizika Tanszek
Physical Review B - Condensed Matter and Materials Physics | Year: 2015

The disorder-induced metal-insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e., in the three conventional symmetry classes. Large-scale numerical simulations have been performed on systems with linear sizes up to L=100 in order to obtain eigenstates at the band center, E=0. The multifractal dimensions, exponents Dq and αq, have been determined in the range of -1≤q≤2. The finite-size scaling of the generalized multifractal exponents provide the critical exponents for the different symmetry classes in accordance with values known from the literature based on high-precision transfer matrix techniques. The multifractal exponents of the different symmetry classes provide further characterization of the Anderson transition, which was missing from the literature so far. © 2015 American Physical Society.


Ujfalusi L.,Elmeleti Fizika Tanszek | Varga I.,Elmeleti Fizika Tanszek
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a nonmonotonic behavior as a function of energy owing to the anomalous behavior of few-site localization. The two-site approximation is solved analytically and is shown to capture the essential features found in numerical simulations on one-, two-, and three-dimensional systems. Further improvement has been obtained by solving a three-site model. © 2012 American Physical Society.


Ujfalusi L.,Elmeleti Fizika Tanszek | Varga I.,Elmeleti Fizika Tanszek
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

The phase diagram of the metal-insulator transition in a three-dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large-scale numerical simulation has been performed on systems with linear sizes up to L=140. The multifractal dimensions, exponents Dq and αq, have been determined in the range of 0≤q≤1. Our results confirm that this problem belongs to the same universality class as the three-dimensional Anderson model; the critical exponent of the localization length was found to be ν=1.622±0.035. However, the multifractal function f(α) and the exponents Dq and αq produced anomalous variations along the phase boundary, pcQ(E). © 2014 American Physical Society.


Ujfalusi L.,Elmeleti Fizika Tanszek | Varga I.,Elmeleti Fizika Tanszek | Schumayer D.,University of Otago
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N→ the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist. © 2011 American Physical Society.

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