45 research outputs found

### Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular
subalgebra of a simple Lie algebra G is used to construct realizations of G.
When G=so(4,2), unitary representations of the conformal and Poincare algebras
are recognized in this approach, which can be compared to the usual induced
representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can
be seen as the eigenvalue of a W generator in such W representations of G. The
generalization of such properties to the affine case is also discussed in the
conclusion, where an alternative of the Wakimoto construction for sl(2) level k
is briefly presented. This mini review is based on invited talks presented by
P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable
Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras
and their Applications to Physics'', Tianjin (China), August 1996; ``Selected
Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia),
September 1996; to be published in the Proceedings.Comment: LaTeX, 16 pages, references adde

### Field theory of anyons in the lowest Landau level

We construct a field theory for anyons in the lowest Landau level starting
from the $N$-particle description, and discuss the connection to the full field
theory of anyons defined using a statistical gauge potential. The theory is
transformed to free form, with the fields defined on the circle and satisfying
modified commutation relations. The Fock space of the anyons is discussed, and
the theory is related to that of edge excitations of an anyon droplet in a
harmonic oscillator well.Comment: 27 pages (incl. 2 figs.) in standard Latex. Substantially revised
version with a section on the connection to Luttinger liquid

### Energy Spectrum of Anyons in a Magnetic Field

For the many-anyon system in external magnetic field, we derive the energy
spectrum as an exact solution of the quantum eigenvalue problem with particular
topological constraints. Our results agree with the numerical spectra recently
obtained for the 3- and the 4-anyon systems.Comment: 11 pages in Plain LaTeX (plus 4 figures available on request), DFPD
92/TH/4

### Charge and Statistics of Quantum Hall Quasi-Particles. A numerical study of mean values and fluctuations

We present Monte Carlo studies of charge expectation values and charge
fluctuations for quasi-particles in the quantum Hall system. We have studied
the Laughlin wave functions for quasi-hole and quasi-electron, and also Jain's
definition of the quasi-electron wave function. The considered systems consist
of from 50 to 200 electrons, and the filling fraction is 1/3. For all
quasi-particles our calculations reproduce well the expected values of charge;
-1/3 times the electron charge for the quasi-hole, and 1/3 for the
quasi-electron. Regarding fluctuations in the charge, our results for the
quasi-hole and Jain quasi-electron are consistent with the expected value zero
in the bulk of the system, but for the Laughlin quasi-electron we find small,
but significant, deviations from zero throughout the whole electron droplet. We
also present Berry phase calculations of charge and statistics parameter for
the Jain quasi-electron, calculations which supplement earlier studies for the
Laughlin quasi-particles. We find that the statistics parameter is more well
behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron.Comment: 39 pages, 27 figure

### Finite Chern-Simons matrix model - algebraic approach

We analyze the algebra of observables and the physical Fock space of the
finite Chern-Simons matrix model. We observe that the minimal algebra of
observables acting on that Fock space is identical to that of the Calogero
model. Our main result is the identification of the states in the l-th tower of
the Chern-Simons matrix model Fock space and the states of the Calogero model
with the interaction parameter nu=l+1. We describe quasiparticle and quasihole
states in the both models in terms of Schur functions, and discuss some
nontrivial consequences of our algebraic approach.Comment: 12pages, jhep cls, minor correction

### Haldane exclusion statistics and second virial coefficient

We show that Haldanes new definition of statistics, when generalised to
infinite dimensional Hilbert spaces, is equal to the high temperature limit of
the second virial coefficient. We thus show that this exclusion statistics
parameter, g , of anyons is non-trivial and is completely determined by its
exchange statistics parameter $\alpha$. We also compute g for quasiparticles in
the Luttinger model and show that it is equal to $\alpha$.Comment: 11 pages, REVTEX 3.

### Exact Multiplicities in the Three-Anyon Spectrum

Using the symmetry properties of the three-anyon spectrum, we obtain exactly
the multiplicities of states with given energy and angular momentum. The
results are shown to be in agreement with the proper quantum mechanical and
semiclassical considerations, and the unexplained points are indicated.Comment: 16 pages plus 3 postscript figures, Kiev Institute for Theoretical
Physics preprint ITP-93-32

### Statistical properties and statistical interaction for particles with spin: Hubbard model in one dimension and statistical spin liquid

We derive the statistical distribution functions for the Hubbard chain with
infinite Coulomb repulsion among particles and for the statistical spin liquid
with an arbitrary magnitude of the local interaction in momentum space.
Haldane's statistical interaction is derived from an exact solution for each of
the two models. In the case of the Hubbard chain the charge (holon) and the
spin (spinon) excitations decouple completely and are shown to behave
statistically as fermions and bosons, respectively. In both cases the
statistical interaction must contain several components, a rule for the
particles with the internal symmetry.Comment: (RevTex, 16 pages, improved version

### Quantumgroups in the Higgs Phase

In the Higgs phase we may be left with a residual finite symmetry group H of
the condensate. The topological interactions between the magnetic- and electric
excitations in these so-called discrete H gauge theories are completely
described by the Hopf algebra or quantumgroup D(H). In 2+1 dimensional space
time we may add a Chern-Simons term to such a model. This deforms the
underlying Hopf algebra D(H) into a quasi-Hopf algebra by means of a 3-cocycle
H. Consequently, the finite number of physically inequivalent discrete H gauge
theories obtained in this way are labelled by the elements of the cohomology
group H^3(H,U(1)). We briefly review the above results in these notes. Special
attention is given to the Coulomb screening mechanism operational in the Higgs
phase. This mechanism screens the Coulomb interactions, but not the
Aharonov-Bohm interactions. (Invited talk given by Mark de Wild Propitius at
`The III International Conference on Mathematical Physics, String Theory and
Quantum Gravity', Alushta, Ukraine, June 13-24, 1993. To be published in Theor.
Math. Phys.)Comment: 19 pages in Latex, ITFA-93-3

### Dynamics of the Compact, Ferromagnetic \nu=1 Edge

We consider the edge dynamics of a compact, fully spin polarized state at
filling factor $\nu=1$. We show that there are two sets of collective
excitations localized near the edge: the much studied, gapless, edge
magnetoplasmon but also an additional edge spin wave that splits off below the
bulk spin wave continuum. We show that both of these excitations can soften at
finite wave-vectors as the potential confining the system is softened, thereby
leading to edge reconstruction by spin texture or charge density wave
formation. We note that a commonly employed model of the edge confining
potential is non-generic in that it systematically underestimates the texturing
instability.Comment: 13 pages, 7 figures, Revte