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

The saturation property for branching rules -- Examples

For a few pairs $G\subset \hat G$ of reductive groups, we study the decomposition of irreducible \hait G-modules into $G$-modules. In particular, we observe the saturation property for all of these pairs.Comment: 22 pages Some proofs use computer computation

Excitonic effects in two-dimensional TiSe2_2 from hybrid density functional theory

Transition metal dichalcogenides (TMDs), whether in bulk or in monolayer form, exhibit a rich variety of charge-density-wave (CDW) phases and stronger periodic lattice distortions. While the actual role of nesting has been under debate, it is well understood that the microscopic interaction responsible for the CDWs is the electron-phonon coupling. The case of TiSe$_2$ is however unique in this family in that the normal state above the critical temperature $T_\mathrm{CDW}$ is characterized by a small quasiparticle bandgap as measured by ARPES, so that no nesting-derived enhancement of the susceptibility is present. It has therefore been argued that the mechanism responsible for this CDW should be different and that this material realizes the excitonic insulator phase proposed by Walter Kohn. On the other hand, it has also been suggested that the whole phase diagram can be explained by a sufficiently strong electron-phonon coupling. In this work, in order to estimate how close this material is to the pure excitonic insulator instability, we quantify the strength of electron-hole interactions by computing the exciton band structure at the level of hybrid density functional theory, focusing on the monolayer. We find that in a certain range of parameters the indirect gap at $q_{\mathrm{CDW}}$ is significantly reduced by excitonic effects. We discuss the consequences of those results regarding the debate on the physical mechanism responsible for this CDW. Based on the dependence of the calculated exciton binding energies as a function of the mixing parameter of hybrid DFT, we conjecture that a necessary condition for a pure excitonic insulator is that its noninteracting electronic structure is metallic.Comment: 6 pages, 3 figure