Boundary Multifractality at the Integer Quantum Hall Plateau Transition: Implications for the Critical Theory

Obuse, Hideaki; Subramaniam, Arvind R.; Furusaki, Akira; Gruzberg, Ilya A.; Ludwig, Andreas

doi:10.1103/physrevlett.101.116802

Cited by 64 publications

(78 citation statements)

References 31 publications

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“…24,29 This is the delocalized state separating adjacent Hall plateaux; it exhibits strong multifractality that has been extensively studied in numerics. 18,[26][27][28] The spectrum is believed to be universal, 18 and is approximately 28 parabolic as in Eqs. (2.3) and (2.5), with θ ∼ 0.26 (Refs.…”

Section: Broken T : Iqhp Transitionmentioning

confidence: 99%

“…24,29 This state exhibits strong multifractality that has been extensively studied in numerics. 18,19,[26][27][28] Fig. 3, but for different unitary class disorder strength combinations.…”

Section: )mentioning

confidence: 99%

“…the diffusive (symplectic) metal 20,23 and the integer quantum Hall plateau transition. 18,[26][27][28] These appear at strong coupling (many impurities) for dirty Dirac fermions. 9,10,24,29 We consider the case of a single flavor Dirac surface band, relevant to (e.g.)…”

Section: Introductionmentioning

confidence: 99%

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Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

Foster

2012

Phys. Rev. B

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We compute the multifractal spectra associated to local density of states (LDOS) fluctuations due to weak quenched disorder, for a single Dirac fermion in two spatial dimensions. Our results are relevant to the surfaces of Z2 topological insulators such as Bi2Se3 and Bi2Te3, where LDOS modulations can be directly probed via scanning tunneling microscopy. We find a qualitative difference in spectra obtained for magnetic versus non-magnetic disorder. Randomly polarized magnetic impurities induce quadratic multifractality at first order in the impurity density; by contrast, no operator exhibits multifractal scaling at this order for a non-magnetic impurity profile. For the time-reversal invariant case, we compute the first non-trivial multifractal correction, which appears at two loops (impurity density squared). We discuss spectral enhancement approaching the Dirac point due to renormalization, and we survey known results for the opposite limit of strong disorder.

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Section: Broken T : Iqhp Transitionmentioning

confidence: 99%

“…24,29 This state exhibits strong multifractality that has been extensively studied in numerics. 18,19,[26][27][28] Fig. 3, but for different unitary class disorder strength combinations.…”

Section: )mentioning

confidence: 99%

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Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

Foster

2012

Phys. Rev. B

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“…The nature of the critical state at and the critical phenomena near the IQH transition are at the focus of intense experimental [8][9][10][11][12][13] and theoretical research. [14][15][16][17][18][19][20][21][22][23] In spite of much effort over several decades, an analytical treatment of most of the critical conducting states in disordered electronic systems, including in particular that of the mentioned IQH transition, has been elusive (although some proposals [14][15][16] have been put forward, but see Refs. 18 and 19).…”

Section: Introductionmentioning

confidence: 99%

Quantum Hall transitions: An exact theory based on conformal restriction

2012

Self Cite

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We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, and for other two-dimensional disordered systems, based on the theory of "conformal restriction". This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the "stochastic geometry" of fractal curves and other stochastic geometrical fractal objects in two-dimensional space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model for the transition. We show that the disorder-averaged PCCs are characterized by a classical probability distribution for certain geometric objects in the plane (which we call pictures), occurring with positive statistical weights, that satisfy the crucial so-called restriction property with respect to changes in the shape of the sample with absorbing boundaries; physically, these are boundaries connected to ideal leads. At the transition point, these geometrical objects (pictures) become fractals. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of "conformal restriction measures" to relate the disorder-averaged PCCs to correlation functions of (Virasoro) primary operators in a conformal field theory (of central charge c = 0). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in two spatial dimensions, including for example the spin quantum Hall effect, the thermal metal phase in symmetry class D, and classical diffusion in two dimensions in a perpendicular magnetic field. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.

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“…In condensed matter physics in the case of the integer quantum Hall effect as well as for disordered systems psl(N|N) symmetry and its central extension gl(N|N) are present [39,40]. Boundary spectra were also computed perturbatively in this context [41].…”

Section: Introductionmentioning

confidence: 99%

Yangian superalgebras in conformal field theory

Creutzig

2011

Nuclear Physics B

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Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;α) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP N−1|N sigma models, while the former are conjecturally dual to supersphere sigma models. *

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Boundary Multifractality at the Integer Quantum Hall Plateau Transition: Implications for the Critical Theory

Cited by 64 publications

References 31 publications

Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

Quantum Hall transitions: An exact theory based on conformal restriction

Yangian superalgebras in conformal field theory

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