57 research outputs found
Duality and Non-linear Response for Quantum Hall Systems
We derive the implications of particle-vortex duality for the electromagnetic
response of Quantum Hall systems beyond the linear-response regime. This
provides a first theoretical explanation of the remarkable duality which has
been observed in the nonlinear regime for the electromagnetic response of
Quantum Hall systems.Comment: 7 pages, 1 figure, typeset in LaTe
An RG potential for the quantum Hall effects
The phenomenological analysis of fully spin-polarized quantum Hall systems,
based on holomorphic modular symmetries of the renormalization group (RG) flow,
is generalized to more complicated situations where the spin or other "flavors"
of charge carriers are relevant, and where the symmetry is different. We make
the simplest possible ansatz for a family of RG potentials that can interpolate
between these symmetries. It is parametrized by a single number and we show
that this suffices to account for almost all scaling data obtained to date. The
potential is always symmetric under the main congruence group at level two, and
when takes certain values this symmetry is enhanced to one of the maximal
subgroups of the modular group. We compute the covariant RG -function,
which is a holomorphic vector field derived from the potential, and compare the
geometry of this gradient flow with available temperature driven scaling data.
The value of is determined from experiment by finding the location of a
quantum critical point, i.e., an unstable zero of the -function given by
a saddle point of the RG potential. The data are consistent with , which together with the symmetry leads to a generalized
semi-circle law.Comment: 10 figures, sligthly updated discussion and refs, accepted for PR
Duality in the Quantum Hall Effect - the Role of Electron Spin
At low temperatures the phase diagram for the quantum Hall effect has a
powerful symmetry arising from the Law of Corresponding States. This symmetry
gives rise to an infinite order discrete group which is a generalisation of
Kramers-Wannier duality for the two dimensional Ising model. The duality group,
which is a subgroup of the modular group, is analysed and it is argued that
there is a quantitative difference between a situation in which the spin
splitting of electron energy levels is comparable to the cyclotron energy and
one in which the spin splitting is much less than the cyclotron energy. In the
former case the group of symmetries is larger than in the latter case. These
duality symmetries are used to constrain the scaling functions of the theory
and, under an assumption of complex meromorphicity, a unique functional form is
obtained for the crossover of the conductivities between Hall states as a
function of the external magnetic field. This analytic form is shown to give
good agreement with experimental data.
The analysis requires a consideration of the way in which longitudinal
resistivities are extracted from the experimentally measured longitudinal
resistances and a novel method is proposed for determining the correct
normalisation for the former.Comment: 22 pages, 8 figures, typeset in LaTe
Derivation of the Semi-circle Law from the Law of Corresponding States
We show that, for the transition between any two quantum Hall states, the
semi-circle law and the existence of a duality symmetry follow solely from the
consistency of the law of corresponding states with the two-dimensional scaling
flow. This puts these two effects on a sound theoretical footing, implying that
both should hold exactly at zero temperature, independently of the details of
the microscopic electron dynamics. This derivation also shows how the
experimental evidence favours taking the two-dimensional flow seriously for the
whole transition, and not just near the critical points.Comment: 4 pages, 1 figure, typeset in LaTeX (uses revtex
Radiative corrections to the Casimir force and effective field theories
Radiative corrections to the Casimir force between two parallel plates are
considered in both scalar field theory of one massless and one massive field
and in QED. Full calculations are contrasted with calculations based on
employing ``boundary-free'' effective field theories. The difference between
two previous results on QED radiative corrections to the Casimir force between
two parallel plates is clarified and the low-energy effective field theory for
the Casimir effect in QED is constructed.Comment: 17 pages, revte
Electromagnetic Response and Approximate SO(5) Symmetry in High-Tc Superconductors
It has been proposed that the effective Hamiltonian describing high T_c
superconductivity in cuprate materials has an approximate SO(5) symmetry
relating the superconducting (SC) and antiferromagnetic (AF) phases of these
systems. We show that robust consequences of this proposal are potentially
large optical conductivities and Raman scattering rates in the AF phase, due to
the electromagnetic response of the doubly-charged pseudo Goldstone bosons
which must exist there. This provides strong constraints on the properties of
the bosons, such as their mass gap and velocity.Comment: 4 pages, 3 figure
Gauge Invariance and the Critical Properties of Quantum Hall Plateaux Transitions
A model consisting of a single massless scalar field with a topological
coupling to a pure gauge field is defined and studied. It possesses an SL(2,Z)
symmetry as a consequence of the gauge invariance. We propose that by adding
impurities the model can be used to describe transitions between Quantum Hall
plateaux. This leads to a correlation length exponent of 20/9, in excellent
agreement with the most recent experimental measurements.Comment: 25 pages, minor changes in data discussion, Section V on connection
with staircase model is expanded References added. Interpretive comments
added in section 3 about the critical condition. with improved terminolog
RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
We determine the exact beta function and a RG flow Lyapunov function for N=2
SYM with gauge group SU(n). It turns out that the classical discriminants of
the Seiberg-Witten curves determine the RG potential. The radial
irreversibility of the RG flow in the SU(2) case and the non-perturbative
identity relating the -modulus and the superconformal anomaly, indicate the
existence of a four dimensional analogue of the c-theorem for N=2 SYM which we
formulate for the full SU(n) theory. Our investigation provides further
evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References
added. Version published in PR
A Vector Non-abelian Chern-Simons Duality
Abelian Chern-Simons gauge theory is known to possess a `-self-dual'
action where its coupling constant is inverted {\it i.e.} . Here a vector non-abelian duality is found in the
pure non-abelian Chern-Simons action at the classical level. The dimensional
reduction of the dual Chern-Simons action to two-dimensions constitutes a dual
Wess-Zumino-Witten action already given in the literature.Comment: 14+1 pages, LaTeX file, no figures, version to appear in Phys. Rev
Duality and Universality for the Chern-Simons bosons
By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg
theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the
Chern-Simons gauge field, we investigate phase transitions of Chern-Simons
bosons in the limit of strong coupling. We construct algebraically exact
duality and flux attachment transformations of the lattice theories,
corresponding to analogous transformations in the continuum limit. These
transformations are used to convert the model with arbitrary fractional
Chern-Simons coefficient to a model with either zero or one.
Depending on this final value of , the phase transition in the original
model is either in the universality class of the 3D x-y model or a
``fermionic'' universality class, unless the irrelevant corrections of cubic
and higher power in momenta render the transition of the first order.Comment: 14 two-column pages, revtex 3.0, multicol and epsf.sty (optional),
one PostScript figure, Submitted to Phys. Rev. B The changes intended to
simplify the arguments and eliminate logical gaps. We also show how the
filling factor is changed by the duality transformatio
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