131 research outputs found
(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.
On the Phase Boundaries of the Integer Quantum Hall Effect. II
It is shown that the statements about the observation of the transitions
between the insulating phase and the integer quantum Hall effect phases with
the quantized Hall conductivity made in a
number of works are unjustified. In these works, the crossing points of the
magnetic field dependences of the diagonal resistivity at different
temperatures at have been misidentified as the
critical points of the phase transitions. In fact, these crossing points are
due to the sign change of the derivative owing to the quantum
corrections to the conductivity.Comment: 3 pages, 2 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
Super universality of the quantum Hall effect and the "large picture" of the angle
It is shown that the "massless chiral edge excitations" are an integral and
universal aspect of the low energy dynamics of the vacuum that has
historically gone unnoticed. Within the
non-linear sigma model we introduce an effective theory of "edge excitations"
that fundamentally explains the quantum Hall effect. In sharp contrast to the
common beliefs in the field our results indicate that this macroscopic
quantization phenomenon is, in fact, a {\em super universal} strong coupling
feature of the angle with the replica limit only playing a
role of secondary importance. To demonstrate super universality we revisit the
large expansion of the model. We obtain, for the first time,
explicit scaling results for the quantum Hall effect including quantum
criticality of the quantum Hall plateau transition. Consequently a scaling
diagram is obtained describing the cross-over between the weak coupling
"instanton phase" and the strong coupling "quantum Hall phase" of the large
theory. Our results are in accordance with the "instanton picture" of the
angle but fundamentally invalidate all the ideas, expectations and
conjectures that are based on the historical "large picture."Comment: 40 pages, 9 figure
The effect of carrier density gradients on magnetotransport data measured in Hall bar geometry
We have measured magnetotransport of the two-dimensional electron gas in a
Hall bar geometry in the presence of small carrier density gradients. We find
that the longitudinal resistances measured at both sides of the Hall bar
interchange by reversing the polarity of the magnetic field. We offer a simple
explanation for this effect and discuss implications for extracting
conductivity flow diagrams of the integer quantum Hall effect.Comment: 7 pages, 8 figure
Probing the plateau-insulator quantum phase transition in the quantum Hall regime
We report quantum Hall experiments on the plateau-insulator transition in a
low mobility In_{.53} Ga_{.47} As/InP heterostructure. The data for the
longitudinal resistance \rho_{xx} follow an exponential law and we extract a
critical exponent \kappa= .55 \pm .05 which is slightly different from the
established value \kappa = .42 \pm .04 for the plateau transitions. Upon
correction for inhomogeneity effects, which cause the critical conductance
\sigma_{xx}^* to depend marginally on temperature, our data indicate that the
plateau-plateau and plateau- insulator transitions are in the same universality
class.Comment: 4 pages, 4 figures (.eps
Renormalization of the vacuum angle in quantum mechanics, Berry phase and continuous measurements
The vacuum angle renormalization is studied for a toy model of a
quantum particle moving around a ring, threaded by a magnetic flux .
Different renormalization group (RG) procedures lead to the same generic RG
flow diagram, similar to that of the quantum Hall effect. We argue that the
renormalized value of the vacuum angle may be observed if the particle's
position is measured with finite accuracy or coupled to additional slow
variable, which can be viewed as a coordinate of a second (heavy) particle on
the ring. In this case the renormalized appears as a magnetic flux
this heavy particle sees, or the Berry phase, associated with its slow
rotation.Comment: 4 pages, 2 figure
The Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions
We study the effects of electron-electron interaction on the critical
properties of the plateau transitions in the {\it integer} quantum Hall effect.
We find the renormalization group dimension associated with short-range
interactions to be . Thus the non-interacting fixed point
(characterized and ) is stable. For the Coulomb
interaction, we find the correlation effect is a marginal perturbation at a
Hartree-Fock fixed point (, ) by dimension counting.
Further calculations are needed to determine its stability upon loop
corrections.Comment: 12 pages, Revtex, minor changes, to be published in Phys. Rev. Let
Exact renormalization-group analysis of first order phase transitions in clock models
We analyze the exact behavior of the renormalization group flow in
one-dimensional clock-models which undergo first order phase transitions by the
presence of complex interactions. The flow, defined by decimation, is shown to
be single-valued and continuous throughout its domain of definition, which
contains the transition points. This fact is in disagreement with a recently
proposed scenario for first order phase transitions claiming the existence of
discontinuities of the renormalization group. The results are in partial
agreement with the standard scenario. However in the vicinity of some fixed
points of the critical surface the renormalized measure does not correspond to
a renormalized Hamiltonian for some choices of renormalization blocks. These
pathologies although similar to Griffiths-Pearce pathologies have a different
physical origin: the complex character of the interactions. We elucidate the
dynamical reason for such a pathological behavior: entire regions of coupling
constants blow up under the renormalization group transformation. The flows
provide non-perturbative patterns for the renormalization group behavior of
electric conductivities in the quantum Hall effect.Comment: 13 pages + 3 ps figures not included, TeX, DFTUZ 91.3
Network Models of Quantum Percolation and Their Field-Theory Representations
We obtain the field-theory representations of several network models that are
relevant to 2D transport in high magnetic fields. Among them, the simplest one,
which is relevant to the plateau transition in the quantum Hall effect, is
equivalent to a particular representation of an antiferromagnetic SU(2N) () spin chain. Since the later can be mapped onto a ,
sigma model, and since recent numerical analyses of the
corresponding network give a delocalization transition with ,
we conclude that the same exponent is applicable to the sigma model
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