653 research outputs found
Multipole Expansion in the Quantum Hall Effect
The effective action for low-energy excitations of Laughlin's states is
obtained by systematic expansion in inverse powers of the magnetic field. It is
based on the W-infinity symmetry of quantum incompressible fluids and the
associated higher-spin fields. Besides reproducing the Wen and Wen-Zee actions
and the Hall viscosity, this approach further indicates that the low-energy
excitations are extended objects with dipolar and multipolar moments.Comment: 29 pages, 5 figures; v2: comments and references adde
A-D-E Classification of Conformal Field Theories
The ADE classification scheme is encountered in many areas of mathematics,
most notably in the study of Lie algebras. Here such a scheme is shown to
describe families of two-dimensional conformal field theories.Comment: 19 pages, 4 figures, 4 tables; review article to appear in
Scholarpedia, http://www.scholarpedia.org
Three-dimensional Topological Insulators and Bosonization
Massless excitations at the surface of three-dimensional time-reversal
invariant topological insulators possess both fermionic and bosonic
descriptions, originating from band theory and hydrodynamic BF gauge theory,
respectively. We analyze the corresponding field theories of the Dirac fermion
and compactified boson and compute their partition functions on the
three-dimensional torus geometry. We then find some non-dynamic exact
properties of bosonization in (2+1) dimensions, regarding fermion parity and
spin sectors. Using these results, we extend the Fu-Kane-Mele stability
argument to fractional topological insulators in three dimensions.Comment: 54 pages, 11 figure
Critical Ising Model in Varying Dimension by Conformal Bootstrap
The single-correlator conformal bootstrap is solved numerically for several
values of dimension 4>d>2 using the available SDPB and Extremal Functional
methods. Critical exponents and other conformal data of low-lying states are
obtained over the entire range of dimensions with up to four-decimal precision
and then compared with several existing results. The conformal dimensions of
leading-twist fields are also determined up to high spin, and their
d-dependence shows how the conformal states rearrange themselves around d=2.2
for matching the Virasoro conformal blocks in the d=2 limit. The decoupling of
states at the Ising point is studied for 3>d>2 and the vanishing of one
structure constant at d=3 is found to persist till d=2 where it corresponds to
a Virasoro null-vector condition.Comment: 43 pages, 15 figures, 7 tables, numerical data and Mathematica files
are available upon request; v2: epsilon-expansion data adde
Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
Chiral conformal field theories are characterized by a ground-state current
at finite temperature, that could be observed, e.g. in the edge excitations of
the quantum Hall effect. We show that the corresponding thermal conductance is
directly proportional to the gravitational anomaly of the conformal theory,
upon extending the well-known relation between specific heat and conformal
anomaly. The thermal current could signal the elusive neutral edge modes that
are expected in the hierarchical Hall states. We then compute the thermal
conductance for the Abelian multi-component theory and the W-infinity minimal
model, two conformal theories that are good candidates for describing the
hierarchical states. Their conductances agree to leading order but differ in
the first, universal finite-size correction, that could be used as a selective
experimental signature.Comment: Latex, 17 pages, 2 figure
Coulomb Blockade in Hierarchical Quantum Hall Droplets
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to
conductance peaks, can be readily derived from the partition functions of
conformal field theory. Their complete expressions can be found for Hall states
with both Abelian and non-Abelian statistics, upon adapting known results for
the annulus geometry. We analyze the Abelian states with hierarchical filling
fractions, \nu=m/(mp \pm 1), and find a non trivial pattern of conductance
peaks. In particular, each one of them occurs with a characteristic
multiplicity, that is due to the extended symmetry of the m-folded edge.
Experimental tests of the multiplicity can shed more light on the dynamics of
this composite edge.Comment: 8 pages; v2: published version; effects of level multiplicities not
well understood, see arXiv:0909.3588 for the correct analysi
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