Critical level spacing distribution of two-dimensional disordered systems with spin-orbit coupling

Schweitzer, L.; Zharekeshev, I. Kh.

doi:10.1088/0953-8984/7/28/002

Cited by 28 publications

(39 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For disorder strength W close to the critical value W c various new scale independent distributions have been discovered recently in several systems [10,11,13,16,17] that exhibit a metal-insulator-transition or at least a critical point. …”

Section: Model and Methodsmentioning

confidence: 99%

See 1 more Smart Citation

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

Batsch

Schweitzer

Krämer

1998

Physica B: Condensed Matter

View full text Add to dashboard Cite

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-s behavior of the nearest neighbor level spacing distribution P (s) and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.

show abstract

Section: Model and Methodsmentioning

confidence: 99%

“…On the other hand, using the method of energy-level statistics [10,11,12,13], system sizes of more than a factor of 10 larger are accessible. In this method, the knowledge of the eigenfunctions is not necessary, because the information about localized, critical or extended states is gained from the spectral correlations.…”

Section: Introductionmentioning

confidence: 99%

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

Batsch

Schweitzer

Krämer

1998

Physica B: Condensed Matter

View full text Add to dashboard Cite

show abstract

“…They are different from random matrix theory and Poisson statistics. The universality of these statistics dubbed "critical level statistics" is also classified by the symmetry of the ensemble [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…[8], it has been suggested that the level spacing distribution may be described by a more generalized form P͑s͒ = As ␣ e −␤s ␥ ͑␣ , ␤ , ␥ Ͼ 0͒. Although this simple form is not valid, the power-law behavior at the origin and the exponential decay in the tail (with ␥ =1) have been observed in numerical studies and classified according to the symmetry of the system [9][10][11][12][13]. A similar rich structure of critical level statistics should be expected for quasiperiodic systems.…”

Section: Introductionmentioning

confidence: 99%

Statistics of spectra for critical quantum chaos in one-dimensional quasiperiodic systems

2004

View full text Add to dashboard Cite

We study spectral statistics of one-dimensional quasiperiodic systems at the metal-insulator transition. Several types of spectral statistics are observed at the critical points, lines, and region. On the critical lines, we find the bandwidth distribution P(B) (w) around the origin (in the tail) to have the form of P(B) (w) approximately w(alpha) [P(B) (w) approximately e(-beta w(gamma) ) ] (alpha,beta,gamma >0) , while in the critical region P(B) (w) approximately w(- alpha') (alpha' >0) . We also find the level spacing distribution to follow an inverse power law P(G) (s) approximately s(-delta) (delta>0) .

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Critical level spacing distribution of two-dimensional disordered systems with spin-orbit coupling

Cited by 28 publications

References 19 publications

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

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

Statistics of spectra for critical quantum chaos in one-dimensional quasiperiodic systems

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

Contact Info

Product

Resources

About