452 research outputs found
Anisotropic conductivity tensor on a half-filled high Landau level
We study two-dimensional interacting electrons in a weak perpendicular
magnetic field with the filling factor and in the presence of a
quenched disorder. As it is known, the unidirectional charge density wave state
can exist near a half-filled high Landau level at low temperatures if disorder
is weak enough. We show that the existence of the unidirectional charge density
wave state at temperature where is the transition temperature
leads to the anisotropic conductivity tensor. We find that the anisotropic part
of conductivity tensor is proportional to below the transition in
accordance with the experimental findings. The order parameter fluctuations
wash out the mean-field cusp at and the conductivity tensor becomes
anisotropic even above the mean-field transition temperature .Comment: RevTeX, 13 pages, 6 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
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