165 research outputs found
Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime
We report new experimental data on the plateau-insulator transition in the
quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By
employing the fundamental symmetries of the quantum transport problem we are
able to disentangle the universal quantum critical aspects of the
magnetoresistance data (critical indices and scaling functions) and the sample
dependent aspects due to macroscopic inhomogeneities. Our new results and
methodology indicate that the previously established experimental value for the
critical index (kappa = 0.42) resulted from an admixture of both universal and
sample dependent behavior. A novel, non-Fermi liquid value is found (kappa =
0.57) along with the leading corrections to scaling. The statement of
self-duality under the Chern Simons flux attachment transformation is verified.Comment: 4 pages, 2 figure
The problem of Coulomb interactions in the theory of the quantum Hall effect
We summarize the main ingredients of a unifying theory for abelian quantum
Hall states. This theory combines the Finkelstein approach to localization and
interaction effects with the topological concept of an instanton vacuum as well
as Chern-Simons gauge theory. We elaborate on the meaning of a new symmetry
( invariance) for systems with an infinitely ranged interaction
potential. We address the renormalization of the theory and present the main
results in terms of a scaling diagram of the conductances.Comment: 9 pages, 3 figures. To appear in Proceedings of the International
Conference "Mesoscopics and Strongly Correlated Electron Systems", July 2000,
Chernogolovka, Russi
Topological oscillations of the magnetoconductance in disordered GaAs layers
Oscillatory variations of the diagonal () and Hall ()
magnetoconductances are discussed in view of topological scaling effects giving
rise to the quantum Hall effect. They occur in a field range without
oscillations of the density of states due to Landau quantization, and are,
therefore, totally different from the Shubnikov-de Haas oscillations. Such
oscillations are experimentally observed in disordered GaAs layers in the
extreme quantum limit of applied magnetic field with a good description by the
unified scaling theory of the integer and fractional quantum Hall effect.Comment: 4 pages, 4 figure
The instanton vacuum of generalized models
It has recently been pointed out that the existence of massless chiral edge
excitations has important strong coupling consequences for the topological
concept of an instanton vacuum. In the first part of this paper we elaborate on
the effective action for ``edge excitations'' in the Grassmannian non-linear sigma model in the presence of the term. This
effective action contains complete information on the low energy dynamics of
the system and defines the renormalization of the theory in an unambiguous
manner. In the second part of this paper we revisit the instanton methodology
and embark on the non-perturbative aspects of the renormalization group
including the anomalous dimension of mass terms. The non-perturbative
corrections to both the and functions are obtained while
avoiding the technical difficulties associated with the idea of {\em
constrained} instantons. In the final part of this paper we present the
detailed consequences of our computations for the quantum critical behavior at
. In the range we find quantum critical
behavior with exponents that vary continuously with varying values of and
. Our results display a smooth interpolation between the physically very
different theories with (disordered electron gas, quantum Hall effect)
and (O(3) non-linear sigma model, quantum spin chains) respectively, in
which cases the critical indices are known from other sources. We conclude that
instantons provide not only a {\em qualitative} assessment of the singularity
structure of the theory as a whole, but also remarkably accurate {\em
numerical} estimates of the quantum critical details (critical indices) at
for varying values of and .Comment: Elsart style, 87 pages, 15 figure
The Quantum Hall Effect: Unified Scaling Theory and Quasi-particles at the Edge
We address two fundamental issues in the physics of the quantum Hall effect:
a unified description of scaling behavior of conductances in the integral and
fractional regimes, and a quasi-particle formulation of the chiral Luttinger
Liquids that describe the dynamics of edge excitations in the fractional
regime.Comment: 11 pages, LateX, 2 figures (not included, available from the
authors), to be published in Proceedings of the International Summer School
on Strongly Correlated Electron Systems, Lajos Kossuth University, Debrecen,
Hungary, Sept 199
Comment on ``Topological Oscillations of the Magnetoconductance in Disordered GaAs Layers''
In a recent Letter, Murzin et. al. [Phys. Rev. Lett., vol. 92, 016802 (2004)]
investigated "instanton effects" in the magneto resistance data taken from
samples with heavily Si-doped GaAs layers at low temperatures. This topological
issue originally arose in the development of a microscopic theory of quantum
Hall effect some 20 years ago. The investigations by Murzin et. al., however,
do not convey the correct ideas on scaling that have emerged over the years in
the general theory of quantum transport.Comment: comment on Phys. Rev. Lett., vol. 92, 016802 (2004
Exact Haldane mapping for all and super universality in spin chains
The low energy dynamics of the anti-ferromagnetic Heisenberg spin chain
in the semiclassical limit is known to map onto the O(3) nonlinear
model with a term in 1+1 dimension. Guided by the underlying
dual symmetry of the spin chain, as well as the recently established
topological significance of "dangling edge spins," we report an {\em exact}
mapping onto the O(3) model that avoids the conventional large
approximation altogether. Our new methodology demonstrates all the super
universal features of the angle concept that previously arose in the
theory of the quantum Hall effect. It explains why Haldane's original ideas
remarkably yield the correct answer in spite of the fundamental complications
that generally exist in the idea of semiclassical expansions
(Mis-)handling gauge invariance in the theory of the quantum Hall effect I: Unifying action and the \nu=1/2 state
We propose a unifying theory for both the integral and fractional quantum
Hall regimes. This theory reconciles the Finkelstein approach to localization
and interaction effects with the topological issues of an instanton vacuum and
Chern-Simons gauge theory. We elaborate on the microscopic origins of the
effective action and unravel a new symmetry in the problem with Coulomb
interactions which we name F-invariance. This symmetry has a broad range of
physical consequences which will be the main topic of future analyses. In the
second half of this paper we compute the response of the theory to
electromagnetic perturbations at a tree level approximation. This is applicable
to the theory of ordinary metals as well as the composite fermion approach to
the half-integer effect. Fluctuations in the Chern-Simons gauge fields are
found to be well behaved only when the theory is F-invariant.Comment: 20 pages, 6 figures; appendix B revised; submitted to Phys.Rev.
(Mis-)handling gauge invariance in the theory of the quantum Hall effect II: Perturbative results
The concept of F-invariance, which previously arose in our analysis of the
integral and half-integral quantum Hall effects, is studied in 2+2\epsilon
spatial dimensions. We report the results of a detailed renormalization group
analysis and establish the renormalizability of the (Finkelstein) action to two
loop order. We show that the infrared behavior of the theory can be extracted
from gauge invariant (F-invariant) quantities only. For these quantities
(conductivity, specific heat) we derive explicit scaling functions. We identify
a bosonic quasiparticle density of states which develops a Coulomb gap as one
approaches the metal-insulator transition from the metallic side. We discuss
the consequences of F-invariance for the strong coupling, insulating regime.Comment: 26 pages, 7 figures; minor modifications; submitted to Phys.Rev.
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