Electron Delocalization by a Magnetic Field in Two Dimensions

Levine, Herbert; Libby, Stephen B.; Pruisken, A. M. M.

doi:10.1103/physrevlett.51.1915

Cited by 323 publications

(299 citation statements)

References 33 publications

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“…It is enough to ensure this property at the two singular points z = 0 and z = 1. The blocks F (1) i (z) are regular at z = 0 and logarithmic at z = 1, whilst the blocks F (2) i (z) are logarithmic at z = 0 and regular at z = 1. It is straightforward to see that in this subspace of functions one can only have 10…”

Section: Knizhhnik-zamolodchikov Equationsmentioning

confidence: 99%

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Disordered Dirac fermions: the marriage of three different approaches

Bhaseen¹,

Caux²,

Kogan³

et al. 2001

Nuclear Physics B

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We compare the critical multipoint correlation functions for twodimensional (massless) Dirac fermions in the presence of a random su(N ) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N = 2 case. We demonstrate that this ménageà trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c = −2 theory of dense polymers. The presence of the c = −2 theory may be seen in all three different treatments of the disorder. PACS: 72.15.Rh, 71.30.+h

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Section: Knizhhnik-zamolodchikov Equationsmentioning

confidence: 99%

“…2 In particular the c = −2 operator correspondence will follow quite naturally. We study the four-point correlation function of the supersymmetric Q-matrix: As may be seen from our more detailed studies in Appendix B, this correlation function may be written in the (off-diagonal) form…”

Section: Dense Polymers and Twist Operatorsmentioning

confidence: 99%

Disordered Dirac fermions: the marriage of three different approaches

Bhaseen¹,

Caux²,

Kogan³

et al. 2001

Nuclear Physics B

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“…Transitions between plateaus have been associated with a quantum critical point 1 . This critical point corresponds to a localization-delocalization transition for the electron's wave-function.…”

Section: Introductionmentioning

confidence: 99%

Correlated quantum percolation in the lowest Landau level

Sandler¹,

Maei²,

Kondev³

2004

Phys. Rev. B

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Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization in the lowest Landau level in the presence of a power-law correlated disorder potential. Careful comparisons between classical and quantum dynamics suggest that the extended Harris criterion is applicable in the quantum case. This leads to a prediction of new localization quantum critical points in integer quantum Hall systems with powerlaw correlated disorder potentials. We demonstrate the stability of these critical points to addition of competing short-range disorder potentials, and discuss possible experimental realizations.

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“…This was motivated by a sigmamodel of localization, which was extensively elaborated by Pruisken et al 38,39 , but the target space geometry does not appear to be rich enough to include the FQHE.…”

Section: Comparison With Other Workmentioning

confidence: 99%

Renormalization-group potential for quantum Hall effects

Nissinen

Lütken

2012

Phys. Rev. B

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The phenomenological analysis of fully spin-polarized quantum Hall systems, based on holomorphic modular symmetries of the renormalization group (RG) flow, is generalized to more complicated situations where the spin or other "flavors" of charge carriers are relevant, and where the symmetry is different. We make the simplest possible ansatz for a family of RG potentials that can interpolate between these symmetries. It is parametrized by a single number a and we show that this suffices to account for almost all scaling data obtained to date. The potential is always symmetric under the main congruence group at level two, and when a takes certain values this symmetry is enhanced to one of the maximal subgroups of the modular group. We compute the covariant RG β-function, which is a holomorphic vector field derived from the potential, and compare the geometry of this gradient flow with available temperature driven scaling data. The value of a is determined from experiment by finding the location of a quantum critical point, i.e., an unstable zero of the β-function given by a saddle point of the RG potential. The data are consistent with a ∈ R, which together with the symmetry leads to a generalized semi-circle law.

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Electron Delocalization by a Magnetic Field in Two Dimensions

Cited by 323 publications

References 33 publications

Disordered Dirac fermions: the marriage of three different approaches

Disordered Dirac fermions: the marriage of three different approaches

Correlated quantum percolation in the lowest Landau level

Renormalization-group potential for quantum Hall effects

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