11,629 research outputs found

### Quantum incompressibility and Razumov Stroganov type conjectures

We establish a correspondence between polynomial representations of the
Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect
wave functions. When the deformation parameter is a third root of unity, the
representation degenerates and the wave functions coincide with the domain wall
boundary condition partition function appearing in the conjecture of A.V.
Razumov and Y.G. Stroganov. In particular, this gives a proof of the
identification of the sum of the entries of a O(n) transfer matrix eigenvector
and a six vertex-model partition function, alternative to that of P. Di
Francesco and P. Zinn-Justin.Comment: latex ihp.tex, 2 files, 1 figure, 28 pages
(http://www-spht.cea.fr/articles/T05/087

### Incompressible representations of the Birman-Wenzl-Murakami algebra

We construct a representation of the Birman-Wenzl-Murakami algebra acting on
a space of polynomials in n variables vanishing when three points coincide.
These polynomials are closely related to the Pfaffian state of the Quantum Hall
Effect and to the components the transfer matrix eigenvector of a O(n) crossing
loop model.Comment: latex bmw.tex, 1 file, 20 pages
(http://www-spht.cea.fr/articles/T05/121

### Quantum transition in bilayer states

I study the possible phase transitions when two layers at filling factor
$\nu_t=1$ are gradually separated. In the bosonic case the system should
undergo a pairing transition from a Fermi liquid to an incompressible state. In
the Fermionic case, the state evolves from an incompressible $(1,1,1)$ state to
a Fermi liquid. I speculate that there is an intermediate phase involving
charge two quasiparticles.Comment: Text modification

### Dipoles at $\nu =1$

We consider the problem of Bosonic particles interacting repulsively in a
strong magnetic field at the filling factor $\nu =1.$ We project the system in
the Lowest Landau Level and map the dynamics into an interacting Fermion
system. We study the resulting Hamiltonian in the Hartree--Fock approximation
in the case of a $\delta$ repulsive potential. The physical picture which
emerges is in agreement with the proposal of N. Read that the composite
Fermions behave as a gas of dipoles. We argue that the consequence of this is
that the composite Fermions interact with screened short range interactions. We
develop a Landau theory which we also expect to describe the physical $\nu
=1/2$ Fermionic state. The Form factor, the effective mass and the conductivity
are analised in this model.Comment: flatex_new vincent.tex, 4 files Proceedings on Composite Fermions and
Confinement Moriond, France 1999-03-01 1999-03-06 March 1-6, 199

### Bethe Ansatz and Q-operator for the open ASEP

In this paper, we look at the asymmetric simple exclusion process with open
boundaries with a current-counting deformation. We construct a two-parameter
family of transfer matrices which commute with the deformed Markov matrix of
the system. We show that these transfer matrices can be factorised into two
commuting matrices with one parameter each, which can be identified with
Baxter's Q-operator, and that for certain values of the product of those
parameters, they decompose into a sum of two commuting matrices, one of which
is the Bethe transfer matrix for a given dimension of the auxiliary space.
Using this, we find the T-Q equation for the open ASEP, and, through functional
Bethe Ansatz techniques, we obtain an exact expression for the dominant
eigenvalue of the deformed Markov matrix.Comment: 46 pages. New version: references updated and typos correcte

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