Anderson Transition, Scaling, and Level Statistics in the Presence of Spin Orbit Coupling

Evangelou, S. N.

doi:10.1103/physrevlett.75.2550

Cited by 82 publications

(77 citation statements)

References 19 publications

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“…Another reason why a large number of numerical simulations of the LSD at the transition 8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 were carried out during the past decade is the controversy that existed over the large-spacing tail of the critical LSD. Conclusive demonstration 12,13,21 that this tail is Poissonian, i.e., that there is no repulsion between the levels with spacings much larger than the mean value, 1 rather than super-Poissonian, 23 implying that repulsion is partially preserved, required a very high accuracy of the simulations.…”

Section: Introductionmentioning

confidence: 99%

Renormalization group approach to energy level statistics at the integer quantum Hall transition

2003

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We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. Previously it was demonstrated that the RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P (G) at energies away from the transition yielded the value of the critical exponent, ν, that agreed with most accurate large-size lattice simulations. To obtain the information about the level statistics from the RG approach, we analyze the evolution of the distribution of phases of the amplitude transmission coefficient upon a step of the RG transformation. From the fixed point of this transformation we extract the critical level spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that away from the transition the LSD crosses over towards the Poisson distribution. Studying the change of the LSD around the QH transition, we check that it indeed obeys scaling behavior. This enables us to use the alternative approach to extracting the critical exponent, based on the LSD, and to find ν = 2.37 ± 0.02 very close to the value established in the literature. This provides additional evidence for the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization-delocalization transition.

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Section: Introductionmentioning

confidence: 99%

Renormalization group approach to energy level statistics at the integer quantum Hall transition

2003

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“…It is well known from the finite-size scaling studies of phase transition that all curves for different sizes should cross at a single point (critical point) for a conventional continuous transition [22]. Two examples for such a transition in the localization problem are the three-dimensional Anderson model [21] and 2D case with spin-orbital interaction [23]. However, Fig.…”

Section: -9007͞98͞80(16)͞3563(4)$1500mentioning

confidence: 99%

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

1998

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We study the localization property of a two-dimensional noninteracting electron gas in the presence of a random magnetic field. The localization length is directly calculated using a transfer matrix technique and finite size scaling analysis. We show strong numerical evidence that the system undergoes a disorder-driven Kosterlitz-Thouless-type metal-insulator transition. We develop a mean field theory which maps the random field system into a two-dimensional XY model. The vortex and antivortex excitations in the XY model correspond to two different kinds of magnetic domains in the random field system. [ S0031-9007(98) There has been a long lasting interest in understanding the localization problem in two-dimensional (2D) systems. According to the scaling theory of localization [1], all states in a 2D system are localized if only scalar random potential is present. However, in the presence of a strong perpendicular magnetic field, where the time reversal symmetry is broken, extended states appear in the center of disorder-broadened Landau bands and give rise to the integer quantum Hall effect (QHE) [2].Recently, Halperin, Lee, and Read [3] and Kalmeyer and Zhang [4] developed an effective Chern-Simons field theory to understand electronic properties of the fractional QHE systems. In their theory the quasiparticles are weakly interacting composite fermions [5] which can be constructed by attaching an even number of flux quanta to electrons under a Chern-Simons transformation. In this simple picture, the fractional QHE can be mapped into the integer QHE for the composite fermion system subject to an effective magnetic field [5]. At the filling factor n f 1 2 , although the effective magnetic field B ‫ء‬ vanishes, composite fermions are subject to the random fluctuations of the gauge field induced by the ordinary impurities [3,4]. Thus, it is important to study the localization properties of noninteracting charged particles in the presence of a random magnetic field to understand the half-filling system. The problem of charged particles moving in a random magnetic field is also relevant to the theoretical studies of high T c models where the gauge field fluctuations play an important role [6].There have been many studies trying to understand the localization problem of noninteracting particles in a random magnetic field with zero mean [7][8][9][10][11][12][13][14][15][16][17][18]. However, the main issue, namely, whether there is metal-insulator transition (MIT), remains controversial. Conclusions from previous numerical studies can be summarized into the following three classes: (i) There exists a MIT with scaling behavior on both metal and insulator sides [15,18], (ii) there exists a MIT; however, the scaling curve is found only on the insulator side [7,8,13], and (iii) all states are localized [9,10]. On the analytic side, the result is also inconclusive. According to the conventional scaling theory of localization, the random flux system belongs to the unitary ensemble, which is described by a nonlinear sigma mo...

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“…However the finite-size scaling method is not suitable for SWNs with high connections since the number of connections grows very rapidly with the SWNs size [7]. The level statistics method is successful in the location of the metal-insulator transition in disorder systems [8,9], but it is not suitable in quasiperiodic systems because the level spacing distribution [10] can not be always written as the crossover of Poisson distribution and Wigner-Dyson distribution.…”

Section: Introductionmentioning

confidence: 99%

von Neumann entropy and localization-delocalization transition of electron states in quantum small-world networks

Gong

Tong

2006

Phys. Rev. E

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The von Neumann entropy for an electron in periodic, disorder and quasiperiodic quantum smallworld networks(QSWNs) are studied numerically. For the disorder QSWNs, the derivative of the spectrum averaged von Neumann entropy is maximal at a certain density of shortcut links p * , which can be as a signature of the localization-delocalization transition of electron states. The transition point p * is agreement with that obtained by the level statistics method. For the quasiperiodic QSWNs, it is found that there are two regions of the potential parameter. The behaviors of electron states in different regions are similar to that of periodic and disorder QSWNs, respectively.

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Anderson Transition, Scaling, and Level Statistics in the Presence of Spin Orbit Coupling

Cited by 82 publications

References 19 publications

Renormalization group approach to energy level statistics at the integer quantum Hall transition

Renormalization group approach to energy level statistics at the integer quantum Hall transition

Kosterlitz-Thouless-Type Metal-Insulator Transition of a 2D Electron Gas in a Random Magnetic Field

von Neumann entropy and localization-delocalization transition of electron states in quantum small-world networks

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