3,020 research outputs found
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
Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry
We show how two-dimensional incompressible quantum fluids and their
excitations can be viewed as edge conformal field theories,
thereby providing an algebraic characterization of incompressibility. The
Kac-Radul representation theory of the algebra leads then to
a purely algebraic complete classification of hierarchical quantum Hall states,
which encompasses all measured fractions. Spin-polarized electrons in
single-layer devices can only have Abelian anyon excitations.Comment: 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/9
On the c-theorem in more than two dimensions
Several pieces of evidence have been recently brought up in favour of the
c-theorem in four and higher dimensions, but a solid proof is still lacking. We
present two basic results which could be useful for this search: i) the values
of the putative c-number for free field theories in any even dimension, which
illustrate some properties of this number; ii) the general form of three-point
function of the stress tensor in four dimensions, which shows some physical
consequences of the c-number and of the other trace-anomaly numbers.Comment: Latex, 7 pages, 1 tabl
Modular Invariant Partition Functions in the Quantum Hall Effect
We study the partition function for the low-energy edge excitations of the
incompressible electron fluid. On an annular geometry, these excitations have
opposite chiralities on the two edges; thus, the partition function takes the
standard form of rational conformal field theories. In particular, it is
invariant under modular transformations of the toroidal geometry made by the
angular variable and the compact Euclidean time. The Jain series of plateaus
have been described by two types of edge theories: the minimal models of the
W-infinity algebra of quantum area-preserving diffeomorphisms, and their
non-minimal version, the theories with U(1)xSU(m) affine algebra. We find
modular invariant partition functions for the latter models. Moreover, we
relate the Wen topological order to the modular transformations and the
Verlinde fusion algebra. We find new, non-diagonal modular invariants which
describe edge theories with extended symmetry algebra; their Hall
conductivities match the experimental values beyond the Jain series.Comment: Latex, 38 pages, 1 table (one minor error has been corrected
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
Effective Chern-Simons Theories of Pfaffian and Parafermionic Quantum Hall States, and Orbifold Conformal Field Theories
We present a pure Chern-Simons formulation of families of interesting
Conformal Field Theories describing edge states of non-Abelian Quantum Hall
states. These theories contain two Abelian Chern-Simons fields describing the
electromagnetically charged and neutral sectors of these models, respectively.
The charged sector is the usual Abelian Chern-Simons theory that successfully
describes Laughlin-type incompressible fluids. The neutral sector is a
2+1-dimensional theory analogous to the 1+1-dimensional orbifold conformal
field theories. It is based on the gauge group O(2) which contains a disconnected group manifold, which is the salient feature of this theory.
At level q, the Abelian theory of the neutral sector gives rise to a symmetry, which is further reduced by imposing the
symmetry of charge-conjugation invariance. The remaining symmetry
of the neutral sector is the origin of the non-Abelian statistics of the
(fermionic) q-Pfaffian states
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