Energy-level statistics and localization of 2d electrons in random magnetic fields

Batsch, M.; Schweitzer, L.; Krämer, B.

doi:10.1016/s0921-4526(98)00316-0

Cited by 24 publications

(23 citation statements)

References 16 publications

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“…Thus the procedures of the extraction of ν from both transformations are technically different, but conceptually similar. In fact, the shape of the critical LSD, obtained from the RG approach, shows systematic deviations from the large-scale simulation results 17,18,19,20,21,22,38,39 which yield the body of LSD very close to the Gaussian unitary random matrix ensemble (GUE). 40 However, the RG flow of the LSD towards the insulator appears to be robust.…”

Section: Introductionmentioning

confidence: 87%

“…1,46 Earlier large-scale simulations of the critical LSD 11,12,14,17,18,19,20,21,22,38,39 satisfy this general requirement. The same holds also for our result, as can be seen in Fig.…”

Section: B Small and Large S Behaviormentioning

confidence: 99%

“…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%

“…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. 13,21 The bulk of numerical work on the level statistics at the transition was carried out for three-dimensional systems 8,9,10,11,12,13,14 for which there exists a mobility edge separating localized and extended states. In two dimensions all the states are localized in the absence of a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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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: 87%

“…1,46 Earlier large-scale simulations of the critical LSD 11,12,14,17,18,19,20,21,22,38,39 satisfy this general requirement. The same holds also for our result, as can be seen in Fig.…”

Section: B Small and Large S Behaviormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2003

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“…Just like in Anderson's problem [2] of a quantum particle subjected to a random scalar potential (only), an important question is whether all (generalised) energy eigenstates are spatially localised or whether some of them are delocalised. Until recently, in the RMFcase the answer to the question has remained controversial within perturbative, quasiclassical, field-theoretical and numerical studies [4,40,32,59,72,6,17,19,51,31,60,71,65,48,16,33]. It is therefore desirable to establish exact localisation/delocalisation results for the RMF-case as has been done for random scalar potentials [10,50,64] (see also [41]).…”

Section: Introductionmentioning

confidence: 99%

Energetic and Dynamic Properties of a Quantum Particle in a Spatially Random Magnetic Field with Constant Correlations along one Direction

Leschke

Warzel

Weichlein

2006

Ann. Henri Poincaré

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ABSTRACT. We consider an electrically charged particle on the Euclidean plane subjected to a perpendicular magnetic field which depends only on one of the two Cartesian co-ordinates. For such a "unidirectionally constant" magnetic field (UMF), which otherwise may be random or not, we prove certain spectral and transport properties associated with the corresponding one-particle Schrödinger operator (without scalar potential) by analysing its "energy-band structure". In particular, for an ergodic random UMF we provide conditions which ensure that the operator's entire spectrum is almost surely absolutely continuous. This implies that, along the direction in which the random UMF is constant, the quantum-mechanical motion is almost surely ballistic, while in the perpendicular direction in the plane one has dynamical localisation. The conditions are verified, for example, for Gaussian and Poissonian random UMF's with non-zero mean-values. These results may be viewed as "random analogues" of results first obtained by A.

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Critical level statistics of a quantum Hall system with Dirichlet boundary conditions

Potempa¹,

Schweitzer²

1998

Ann. Phys.

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We investigate numerically the inuence of Dirichlet boundary conditions on the nearest neighbor level spacing distribution P (s) o f a t wo-dimensional disordered tightbinding model in the presence of a strong perpendicular magnetic eld. From the calculation of the second moment o f P (s) it is shown that for Dirichlet boundary conditions, due to the presence of edge states, the position of the critical energy shifts with increasing system size to the location of the critical energy for periodic boundary conditions. An extrapolation to innite system size results in dierent critical (scale independent) P (s) distributions for periodic and Dirichlet boundary conditions.

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Energy-level statistics and localization of 2d electrons in random magnetic fields

Cited by 24 publications

References 16 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

Energetic and Dynamic Properties of a Quantum Particle in a Spatially Random Magnetic Field with Constant Correlations along one Direction

Critical level statistics of a quantum Hall system with Dirichlet boundary conditions

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