3,252 research outputs found
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
A Unified Conformal Field Theory Description of Paired Quantum Hall States
The wave functions of the Haldane-Rezayi paired Hall state have been
previously described by a non-unitary conformal field theory with central
charge c=-2. Moreover, a relation with the c=1 unitary Weyl fermion has been
suggested. We construct the complete unitary theory and show that it
consistently describes the edge excitations of the Haldane-Rezayi state.
Actually, we show that the unitary (c=1) and non-unitary (c=-2) theories are
related by a local map between the two sets of fields and by a suitable change
of conjugation. The unitary theory of the Haldane-Rezayi state is found to be
the same as that of the 331 paired Hall state. Furthermore, the analysis of
modular invariant partition functions shows that no alternative unitary
descriptions are possible for the Haldane-Rezayi state within the class of
rational conformal field theories with abelian current algebra. Finally, the
known c=3/2 conformal theory of the Pfaffian state is also obtained from the
331 theory by a reduction of degrees of freedom which can be physically
realized in the double-layer Hall systems.Comment: Latex, 42 pages, 2 figures, 3 tables; minor corrections to text and
reference
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
A universal conformal field theory approach to the chiral persistent currents in the mesoscopic fractional quantum Hall states
We propose a general and compact scheme for the computation of the periods
and amplitudes of the chiral persistent currents, magnetizations and magnetic
susceptibilities in mesoscopic fractional quantum Hall disk samples threaded by
Aharonov--Bohm magnetic field. This universal approach uses the effective
conformal field theory for the edge states in the quantum Hall effect to derive
explicit formulas for the corresponding partition functions in presence of
flux. We point out the crucial role of a special invariance condition for the
partition function, following from the Bloch-Byers-Yang theorem, which
represents the Laughlin spectral flow. As an example we apply this procedure to
the Z_k parafermion Hall states and show that they have universal non-Fermi
liquid behavior without anomalous oscillations. For the analysis of the
high-temperature asymptotics of the persistent currents in the parafermion
states we derive the modular S-matrices constructed from the S matrices for the
u(1) sector and that for the neutral parafermion sector which is realized as a
diagonal affine coset.Comment: 45 pages, LaTeX2e, 4 EPS figures, 1 table, for related color figures
see http://theo.inrne.bas.bg/~lgeorg/PF_k.htm
A note on the topological order of noncommutative Hall fluids
We evaluate the ground state degeneracy of noncommutative Chern-Simons models
on the two-torus, a quantity that is interpreted as the "topological order" of
associated phases of Hall fluids. We define the noncommutative theory via
T-duality from an ordinary Chern-Simons model with non-abelian 't Hooft
magnetic fluxes. Motivated by this T-duality, we propose a discrete family of
noncommutative, non-abelian fluid models, arising as a natural generalization
of the standard noncommutative Chern-Simons effective models. We compute the
topological order for these universality classes, and comment on their possible
microscopic interpretation.Comment: 14 page
Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
We argue that when conformal symmetry is spontaneously broken the trace
anomalies in the broken and unbroken phases are matched. This puts strong
constraints on the various couplings of the dilaton. Using the uniqueness of
the effective action for the Goldstone supermultiplet for broken
superconformal symmetry the dilaton effective action is calculated.Comment: 29 pages, 2 figure
Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux
Using the effective conformal field theory for the quantum Hall edge states
we propose a compact and convenient scheme for the computation of the periods,
amplitudes and temperature behavior of the chiral persistent currents and the
magnetic susceptibilities in the mesoscopic disk version of the Z_k parafermion
quantum Hall states in the second Landau level. Our numerical calculations show
that the persistent currents are periodic in the Aharonov-Bohm flux with period
exactly one flux quantum and have a diamagnetic nature. In the high-temperature
regime their amplitudes decay exponentially with increasing the temperature and
the corresponding exponents are universal characteristics of non-Fermi liquids.
Our theoretical results for these exponents are in perfect agreement with those
extracted from the numerical data and demonstrate that there is in general a
non-trivial contribution coming from the neutral sector. We emphasize the
crucial role of the non-holomorphic factors, first proposed by Cappelli and
Zemba in the context of the conformal field theory partition functions for the
quantum Hall states, which ensure the invariance of the annulus partition
function under the Laughlin spectral flow.Comment: 14 pages, RevTeX4, 7 figures (eps
Composite Fermion Wavefunctions Derived by Conformal Field Theory
The Jain theory of hierarchical Hall states is reconsidered in the light of
recent analyses that have found exact relations between projected Jain
wavefunctions and conformal field theory correlators. We show that the
underlying conformal theory is precisely given by the W-infinity minimal models
introduced earlier. This theory involves a reduction of the multicomponent
Abelian theory that is similar to the projection to the lowest Landau level in
the Jain approach. The projection yields quasihole excitations obeying
non-Abelian fractional statistics. The analysis closely parallels the bosonic
conformal theory description of the Pfaffian and Read-Rezayi states.Comment: 4 pages, 1 figur
Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers
We demonstrate that the differential magnetic susceptibility of a fractional
quantum Hall disk, representing a Coulomb island in a Fabry--Perot
interferometer, is exactly proportional to the island's conductance and its
paramagnetic peaks are the equilibrium counterparts of the Coulomb blockade
conductance peaks. Using as a thermodynamic potential the partition functions
of the edge states' effective conformal field theory we find the positions of
the Coulomb blockade peaks, when the area of the island is varied, the
modulations of the distance between them as well as the thermal decay and
broadening of the peaks when temperature is increased. The finite-temperature
estimates of the peak's heights and widths could give important information
about the experimental observability of the Coulomb blockade. In addition, the
predicted peak asymmetry and displacement at finite temperature due to neutral
multiplicities could serve to distinguish different fractional quantum Hall
states with similar zero-temperature Coulomb blockade patterns.Comment: 6 pages, 6 figures; published versio
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