318 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
(Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics
The concepts of an instanton vacuum and F-invariance are used to derive a
complete effective theory of massless edge excitations in the quantum Hall
effect. We establish, for the first time, the fundamental relation between the
instanton vacuum approach and the theory of chiral edge bosons. Two
longstanding problems of smooth disorder and Coulomb interactions are
addressed. We introduce a two dimensional network of chiral edge states and
tunneling centers (saddlepoints) as a model for the plateau transitions. We
derive a mean field theory including the Coulomb interactions and explain the
recent empirical fits to transport at low temperatures. Secondly, we address
the problem of electron tunneling into the quantum Hall edge. We express the
problem in terms of an effective Luttinger liquid with conductance parameter
(g) equal to the filling fraction (\nu) of the Landau band. Hence, even in the
integral regime our results for tunneling are completely non-Fermi liquid like,
in sharp contrast to the predictions of single edge theories.Comment: 51 pages, 8 figures; section IIA3 completely revised, section IIB and
appendix C corrected; submitted to Phys.Rev.
The fractional quantum Hall effect: Chern-Simons mapping, duality, Luttinger liquids and the instanton vacuum
We derive, from first principles, the complete Luttinger liquid theory of
abelian quantum Hall edge states. This theory includes the effects of disorder
and Coulomb interactions as well as the coupling to external electromagnetic
fields. We introduce a theory of spatially separated (individually conserved)
edge modes, find an enlarged dual symmetry and obtain a complete classification
of quasiparticle operators and tunneling exponents. The chiral anomaly on the
edge and Laughlin's gauge argument are used to obtain unambiguously the Hall
conductance. In resolving the problem of counter flowing edge modes, we find
that the long range Coulomb interactions play a fundamental role. In order to
set up a theory for arbitrary filling fractions we use the idea of a two
dimensional network of percolating edge modes. We derive an effective, single
mode Luttinger liquid theory for tunneling processes into the quantum Hall edge
which yields a continuous tunneling exponent . The network approach is
also used to re-derive the instanton vacuum or -theory for the plateau
transitions.Comment: 36 pages, 7 figures (eps
Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime
The renormalization theory of the quantum Hall effect relies primarily on the
non-perturbative concept of theta renormalization by instantons. Within the
generalized non-linear sigma model approach initiated by Finkelstein we obtain
the physical observables of the interacting electron gas, formulate the general
(topological) principles by which the Hall conductance is robustly quantized
and derive - for the first time - explicit expressions for the non-perturbative
(instanton) contributions to the renormalization group beta- and gamma-
functions. Our results are in complete agreement with the recently proposed
idea of super universality which says that the fundamental aspects of the
quantum Hall effect are all generic features the instanton vacuum concept in
asymptotically free field theory.Comment: ReVTeX, 38 pages, 9 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
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
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
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
- …