Hierarchy wave functions--from conformal correlators to Tao-Thouless states

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.Comment: 9 page

Search for localized Wannier functions of topological band structures via compressed sensing

We investigate the interplay of band structure topology and localization properties of Wannier functions. To this end, we extend a recently proposed compressed sensing based paradigm for the search for maximally localized Wannier functions [Ozolins et al., Proc. Natl. Acad. Sci. USA 110, 18368 (2013)]. We develop a practical toolbox that enables the search for maximally localized Wannier functions which exactly obey the underlying physical symmetries of a translationally invariant quantum lattice system under investigation. Most saliently, this allows us to systematically identify the most localized representative of a topological equivalence class of band structures, i.e., the most localized set of Wannier functions that is adiabatically connected to a generic initial representative. We also elaborate on the compressed sensing scheme and find a particularly simple and efficient implementation in which each step of the iteration is an O(NlogN) algorithm in the number of lattice sites N. We present benchmark results on one-dimensional topological superconductors demonstrating the power of these tools. Furthermore, we employ our method to address the open question of whether compact Wannier functions can exist for symmetry-protected topological states such as topological insulators in two dimensions. The existence of such functions would imply exact flat-band models with finite range hopping. Here, we find numerical evidence for the absence of such functions. We briefly discuss applications in dissipative-state preparation and in devising variational sets of states for tensor network methods

Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries

We report a systematic study of the fractional quantum Hall effect (FQHE) using the density-matrix renormalization group (DMRG) method on two different geometries: the sphere and the cylinder. We provide convergence benchmarks based on model Hamiltonians known to possess exact zero-energy ground states, as well as an analysis of the number of sweeps and basis elements that need to be kept in order to achieve the desired accuracy.The ground state energies of the Coulomb Hamiltonian at $\nu=1/3$ and $\nu=5/2$ filling are extracted and compared with the results obtained by previous DMRG implementations in the literature. A remarkably rapid convergence in the cylinder geometry is noted and suggests that this boundary condition is particularly suited for the application of the DMRG method to the FQHE.Comment: 5 pages, 7 figure

Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory

We analyze the non-abelian Read-Rezayi quantum Hall states on the torus, where it is natural to employ a mapping of the many-body problem onto a one-dimensional lattice model. On the thin torus--the Tao-Thouless (TT) limit--the interacting many-body problem is exactly solvable. The Read-Rezayi states at filling $\nu=\frac k {kM+2}$ are known to be exact ground states of a local repulsive $k+1$-body interaction, and in the TT limit this is manifested in that all states in the ground state manifold have exactly $k$ particles on any $kM+2$ consecutive sites. For $M\neq 0$ the two-body correlations of these states also imply that there is no more than one particle on $M$ adjacent sites. The fractionally charged quasiparticles and quasiholes appear as domain walls between the ground states, and we show that the number of distinct domain wall patterns gives rise to the nontrivial degeneracies, required by the non-abelian statistics of these states. In the second part of the paper we consider the quasihole degeneracies from a conformal field theory (CFT) perspective, and show that the counting of the domain wall patterns maps one to one on the CFT counting via the fusion rules. Moreover we extend the CFT analysis to topologies of higher genus.Comment: 15 page

The Mitochondrial Genome and Transcriptome of the Basal Dinoflagellate Hematodinium sp.: Character Evolution within the Highly Derived Mitochondrial Genomes of Dinoflagellates

The sister phyla dinoflagellates and apicomplexans inherited a drastically reduced mitochondrial genome (mitochondrial DNA, mtDNA) containing only three protein-coding (cob, cox1, and cox3) genes and two ribosomal RNA (rRNA) genes. In apicomplexans, single copies of these genes are encoded on the smallest known mtDNA chromosome (6 kb). In dinoflagellates, however, the genome has undergone further substantial modifications, including massive genome amplification and recombination resulting in multiple copies of each gene and gene fragments linked in numerous combinations. Furthermore, protein-encoding genes have lost standard stop codons, trans-splicing of messenger RNAs (mRNAs) is required to generate complete cox3 transcripts, and extensive RNA editing recodes most genes. From taxa investigated to date, it is unclear when many of these unusual dinoflagellate mtDNA characters evolved. To address this question, we investigated the mitochondrial genome and transcriptome character states of the deep branching dinoflagellate Hematodinium sp. Genomic data show that like later-branching dinoflagellates Hematodinium sp. also contains an inflated, heavily recombined genome of multicopy genes and gene fragments. Although stop codons are also lacking for cox1 and cob, cox3 still encodes a conventional stop codon. Extensive editing of mRNAs also occurs in Hematodinium sp. The mtDNA of basal dinoflagellate Hematodinium sp. indicates that much of the mtDNA modification in dinoflagellates occurred early in this lineage, including genome amplification and recombination, and decreased use of standard stop codons. Trans-splicing, on the other hand, occurred after Hematodinium sp. diverged. Only RNA editing presents a nonlinear pattern of evolution in dinoflagellates as this process occurs in Hematodinium sp. but is absent in some later-branching taxa indicating that this process was either lost in some lineages or developed more than once during the evolution of the highly unusual dinoflagellate mtDNA

Transient Nature of Long-Term Nonprogression and Broad Virus-Specific Proliferative T-Cell Responses with Sustained Thymic Output in HIV-1 Controllers

HIV-1(+) individuals who, without therapy, conserve cellular anti-HIV-1 responses, present with high, stable CD4(+) T-cell numbers, and control viral replication, facilitate analysis of atypical viro-immunopathology. In the absence of universal definition, immune function in such HIV controllers remains an indication of non-progression.CD4 T-cell responses to a number of HIV-1 proteins and peptide pools were assessed by IFN-gamma ELISpot and lymphoproliferative assays in HIV controllers and chronic progressors. Thymic output was assessed by sjTRECs levels. Follow-up of 41 HIV-1(+) individuals originally identified as "Long-term non-progressors" in 1996 according to clinical criteria, and longitudinal analysis of two HIV controllers over 22 years, was also performed. HIV controllers exhibited substantial IFN-gamma producing and proliferative HIV-1-specific CD4 T-cell responses to both recombinant proteins and peptide pools of Tat, Rev, Nef, Gag and Env, demonstrating functional processing and presentation. Conversely, HIV-specific T-cell responses were limited to IFN-gamma production in chronic progressors. Additionally, thymic output was approximately 19 fold higher in HIV controllers than in age-matched chronic progressors. Follow-up of 41 HIV-1(+) patients identified as LTNP in 1996 revealed the transitory characteristics of this status. IFN-gamma production and proliferative T-cell function also declines in 2 HIV controllers over 22 years.Although increased thymic output and anti-HIV-1 T-cell responses are observed in HIV controllers compared to chronic progressors, the nature of nonprogressor/controller status appears to be transitory

Genome Fragmentation Is Not Confined to the Peridinin Plastid in Dinoflagellates

When plastids are transferred between eukaryote lineages through series of endosymbiosis, their environment changes dramatically. Comparison of dinoflagellate plastids that originated from different algal groups has revealed convergent evolution, suggesting that the host environment mainly influences the evolution of the newly acquired organelle. Recently the genome from the anomalously pigmented dinoflagellate Karlodinium veneficum plastid was uncovered as a conventional chromosome. To determine if this haptophyte-derived plastid contains additional chromosomal fragments that resemble the mini-circles of the peridin-containing plastids, we have investigated its genome by in-depth sequencing using 454 pyrosequencing technology, PCR and clone library analysis. Sequence analyses show several genes with significantly higher copy numbers than present in the chromosome. These genes are most likely extrachromosomal fragments, and the ones with highest copy numbers include genes encoding the chaperone DnaK(Hsp70), the rubisco large subunit (rbcL), and two tRNAs (trnE and trnM). In addition, some photosystem genes such as psaB, psaA, psbB and psbD are overrepresented. Most of the dnaK and rbcL sequences are found as shortened or fragmented gene sequences, typically missing the 3′-terminal portion. Both dnaK and rbcL are associated with a common sequence element consisting of about 120 bp of highly conserved AT-rich sequence followed by a trnE gene, possibly serving as a control region. Decatenation assays and Southern blot analysis indicate that the extrachromosomal plastid sequences do not have the same organization or lengths as the minicircles of the peridinin dinoflagellates. The fragmentation of the haptophyte-derived plastid genome K. veneficum suggests that it is likely a sign of a host-driven process shaping the plastid genomes of dinoflagellates

Magnetic crystals and helical liquids in alkaline-earth fermionic gases

The joint action of a synthetic gauge potential and of atomic contact repulsion in a one-dimensional alkaline-earth(-like) fermionic gas with nuclear spin I leads to the existence of a hierarchy of fractional insulating and conducting states with intriguing properties. We unveil the existence and the features of those phases by means of both analytical bosonization techniques and numerical methods based on the density-matrix renormalization group algorithm. In particular, we show that the gapless phases can support helical modes, whereas the gapped states, which appear under certain conditions, are characterised both by density and magnetic order. Several distinct features emerge solely for spin I larger than 1/2, thus making their study with cold-atoms unique. We will finally argue that these states are related to the properties of an unconventional fractional quantum Hall effect in the thin-torus limit. The properties of this hierarchy of states can be experimentally studied in state-of-the-art cold-atom laboratories

MYB suppresses differentiation and apoptosis of human breast cancer cells

Introduction: MYB is highly expressed in estrogen receptor positive (ER + ve) breast tumours and tumour cell lines. We recently demonstrated that MYB is essential for the proliferation of ER + ve breast cancer cells, and have now investigated its role in mammary epithelial differentiation.Methods: MCF-7 breast cancer cells were treated with sodium butyrate, vitamin E succinate or 12-O-tetradecanoylphorbol-13-acetate to induce differentiation as measured by Nile Red staining of lipid droplets and β-casein expression. The non-tumorigenic murine mammary epithelial cell (MEC) line, HC11, was induced to differentiate with lactogenic hormones. MYB levels were manipulated by inducible lentiviral shRNA-mediated knockdown and retroviral overexpression.Results: We found that MYB expression decreases following chemically-induced differentiation of the human breast cancer cell line MCF-7, and hormonally-induced differentiation of a non-tumorigenic murine mammary epithelial cell (MEC) line, HC11. We also found that shRNA-mediated MYB knockdown initiated differentiation of breast cancer cells, and greatly sensitised them to the differentiative and pro-apoptotic effects of differentiation-inducing agents (DIAs). Sensitisation to the pro-apoptotic effects DIAs is mediated by decreased expression of BCL2, which we show here is a direct MYB target in breast cancer cells. Conversely, enforced expression of MYB resulted in the cells remaining in an undifferentiated state, with concomitant suppression of apoptosis, in the presence of DIAs.Conclusions: Taken together, these data imply that MYB function is critical in regulating the balance between proliferation, differentiation, and apoptosis in MECs. Moreover, our findings suggest MYB may be a viable therapeutic target in breast cancer and suggest specific approaches for exploiting this possibility