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V. Pasquier

Publications and source records attributed to V. Pasquier.

28 records · Page 2Linked to original sources
arXiv1999

Dipoles and fractional quantum Hall masses

We develop a microscopic formalism to study the fractional quantum Hall plateaus at filling factors $ν$ away from $1/2β$ $β$ an integer. The theory is in terms of quasiparticles which carry a charge $e^{\ast}$ equal to $1-2βν$ times the charge of the electron. The wave functions obtained following our approach are shown to coincide precisely with the form predicted by Jain and this holds independently of the interaction potential.\ Microscopically this rigidity originates from the fact that two different charges interacting attractively in their lowest Landau levels form a bound state with a universal wave function. From the expressions of the gaps we compute an effective mass which agrees well with the experiments carried at $ν=1/2$ and 1/4.

cond-mat.mes-hall↗
arXiv1999

Dipoles at $ν=1$

We consider the problem of Bosonic particles interacting repulsively in a strong magnetic field at the filling factor $ν=1.$ 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 $δ$ 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 $ν=1/2$ Fermionic state. The Form factor, the effective mass and the conductivity are analised in this model.

cond-mat↗
arXiv1997

A dipole interpretation of the $ν=1/2$ state

We consider the problem of Bosonic particles interacting repulsively in a strong magnetic field at the filling factor $ν=1$. We project the system in the Lowest Landau Level and set up a formalism to map the dynamics into an interacting Fermion system. Within a mean field approximation we find that the composite Fermions behave as a gas of neutral dipoles and we expect that the low energy limit also describes the physical $ν=1/2$ Fermionic state.

cond-mat↗
arXiv1995

Single particle Green's function in the Calogero-Sutherland model for rational couplings $β=p/q$

We derive an exact expression for the single particle Green function in the Calogero-Sutherland model for all rational values of the coupling $β$. The calculation is based on Jack polynomial techniques and the results are given in the thermodynamical limit. Two type of intermediate states contribute. The firts one consists of a particle propagating out of the Fermi sea and the second one consists of a particle propagating in one direction, q particles in the opposite direction and p holes.

hep-th↗
arXiv1994

A lecture on the Calogero-Sutherland models

In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor of the density operator. 2) The Dunkl operators and their relations with monodromy matrices, Yangians and affine-Hecke algebras. 3) The Haldane-Shastry chain in connection with the Calogero-Sutherland Hamiltonian at a specific coupling constant.

hep-th↗
arXiv1994

Spinons in Conformal Field Theory

We study the $su(2)$ conformal field theory in its spinon description, adapted to the Yangian invariance. By evaluating the action of the Yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with $su(2)$ spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible Yangian multiplet, and also to exhibit operators creating the $N$-spinon highest weight vectors.

hep-th↗
arXiv1994

A simple construction of elliptic $R$-matrices

We show that Belavin's solutions of the quantum Yang--Baxter equation can be obtained by restricting an infinite $R$-matrix to suitable finite dimensional subspaces. This infinite $R$-matrix is a modified version of the Shibukawa--Ueno $R$-matrix acting on functions of two variables.

hep-th↗
arXiv1993

Yang-Baxter equation in spin chains with long range interactions

We consider the $ su(n) $ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.

hep-th↗