Decomposition of fractional quantum Hall states: New symmetries and approximations

We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained without exact diagonalization through a differential equation method that we conjecture to be generic to other FQH model states. The symmetry rules in Ref. 1 as well as the ones we obtain for the spin singlet states allow us to build approximations of FQH states that exhibit increasing overlap with the exact state (as a function of system size). We show that these overlaps reach unity in the thermodynamic limit even though our approximation omits more than half of the Hilbert space. We show that the product rule is valid for any FQH state which can be written as an expectation value of parafermionic operators.Comment: 22 pages, 8 figure

Relating Jack wavefunctions to WA_{k-1} theories

The (k,r)-admissible Jack polynomials, recently proposed as many-body wavefunctions for non-Abelian fractional quantum Hall systems, have been conjectured to be related to some correlation functions of the minimal model WA_{k-1}(k+1,k+r) of the WA_{k-1} algebra. By studying the degenerate representations of the WA_{k-1}(k+1,k+r) theory, we provide a proof for this conjecture.Comment: 13 pages. Published versio

The Indris have got rhythm! Timing and pitch variation of a primate song examined between sexes and age classes

A crucial, common feature of speech and music is that they show non-random structures over time. It is an open question which of the other species share rhythmic abilities with humans, but in most cases the lack of knowledge about their behavioral displays prevents further studies. Indris are the only lemurs who sing. They produce loud howling cries that can be heard at several kilometers, in which all members of a group usually sing. We tested whether overlapping and turn-taking during the songs followed a precise pattern by analysing the temporal structure of the individuals' contribution to the song. We found that both dominants (males and females) and non-dominants influenced the onset timing one another. We have found that the dominant male and the dominant female in a group overlapped each other more frequently than they did with the non-dominants. We then focused on the temporal and frequency structure of particular phrases occurring during the song. Our results show that males and females have dimorphic inter-onset intervals during the phrases. Moreover, median frequencies of the unit emitted in the phrases also differ between the sexes, with males showing higher frequencies when compared to females. We have not found an effect of age on the temporal and spectral structure of the phrases. These results indicate that singing in indris has a high behavioral flexibility and varies according to social and individual factors. The flexible spectral structure of the phrases given during the song may underlie perceptual abilities that are relatively unknown in other non-human primates, such as the ability to recognize particular pitch patterns

Optical signatures of quantum phase transitions in a light-matter system

Information about quantum phase transitions in conventional condensed matter systems, must be sought by probing the matter system itself. By contrast, we show that mixed matter-light systems offer a distinct advantage in that the photon field carries clear signatures of the associated quantum critical phenomena. Having derived an accurate, size-consistent Hamiltonian for the photonic field in the well-known Dicke model, we predict striking behavior of the optical squeezing and photon statistics near the phase transition. The corresponding dynamics resemble those of a degenerate parametric amplifier. Our findings boost the motivation for exploring exotic quantum phase transition phenomena in atom-cavity, nanostructure-cavity, and nanostructure-photonic-band-gap systems.Comment: 4 pages, 4 figure

Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux

We study charged spin-1/2 particles in two dimensions, subject to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying particular attention to the role of the total angular momentum J = L +S. After this we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state leads to the formation of charged spin-textures, which in the simplest cases can be identified with quantum Hall Skyrmions.Comment: 24 pages, 10 figures (with corrected legends

Entanglement Entropy of Random Fractional Quantum Hall Systems

The entanglement entropy of the $\nu = 1/3$ and $\nu = 5/2$ quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the fluctuation in the entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a clear signature of a transition as a function of the disorder strength for the $\nu = 5/2$ state. Prospects for using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.Comment: 29 pages, 16 figures; fixed figures and figure captions; revised fluctuation calculation

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

SQM 2006: Theory Summary and Perspectives

In this write-up of my SQM 2006 Theory Summary talk I focus on a selection of key contributions which I consider to have a large impact on the current status of the field of strangeness physics or which may have the potential to significantly advance strangeness -- or in general flavor physics -- in the near future.Comment: 16 pages, 4 figures, SQM 2006 proceedings. Revised version containing two modifications to the transport theory sectio

Myoclonic status epilepticus and cerebellar hypoplasia associated with a novel variant in the GRIA3 gene

AMPA-type glutamate receptors (AMPARs) are postsynaptic ionotropic receptors which mediate fast excitatory currents. AMPARs have a heterotetrameric structure, variably composed by the four subunits GluA1-4 which are encoded by genes GRIA1-4. Increasing evidence support the role of pathogenic variants in GRIA1-4 genes as causative for syndromic intellectual disability (ID). We report an Italian pedigree where some male individuals share ID, seizures and facial dysmorphisms. The index subject was referred for severe ID, myoclonic seizures, cerebellar signs and short stature. Whole exome sequencing identified a novel variant in GRIA3, c.2360A > G, p.(Glu787Gly). The GRIA3 gene maps to chromosome Xq25 and the c.2360A > G variant was transmitted by his healthy mother. Subsequent analysis in the family showed a segregation pattern compatible with the causative role of this variant, further supported by preliminary functional insights. We provide a detailed description of the clinical evolution of the index subjects and stress the relevance of myoclonic seizures and cerebellar syndrome as cardinal features of his presentation

Instanton moduli spaces and bases in coset conformal field theory

Recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties, one of them is the complete factorization of the coefficients of the operator product expansion. We consider a particular case of the U(r) gauge theory on C^2/Z_p which corresponds to a certain coset conformal field theory and describe the properties of this basis. We argue that in the case p=2, r=2 there exist different bases. We give an explicit construction of one of them. For another basis we propose the formula for matrix elements.Comment: 31 pages, 3 figure