Strongly Correlated Systems Under High Magnetic Field: A Mixed Landau Levels Description for Fractional Quantum Hall Effect

Strong correlation among electrons under high magnetic field gives rise to an entirely new arena of emergent physics, namely fractional quantum Hall effect. Such systems have entirely different elementary degrees of freedom and generally, demand non-perturbative approaches to develop a better understanding. In the literature, there are several analytical methodologies and numerical toolkits available to study such a system. Clustering of zeros, parent Hamiltonian, off-diagonal order parameter, parton construction, matrix product states are to be named among a few of those popular methodologies in the existing literature. Most of these methods work well in the lowest Landau level or holomorphic wavefunction framework. It is, however, imperative to develop such methodology to study systems with Landau levels mixing to study more exotic as well as experimentally relevant states. In this work, we have developed particular methodologies, which denounce the traditional importance of the analytic properties of first quantized model wavefunction thereby extend the existing parent Hamiltonian, topological order-parameter, matrix product states descriptions to mixed Landau level systems. Such extension produces a deeper, compact and holistic understanding of universal physics of exotic phases in strongly correlated systems from the microscopic viewpoint, as well as produces interesting new results. Our second quantized/ non-analytic approach allows us to construct the ``entangled Pauli principle , a guidebook to extract universal/topological properties such as braiding statistics, fractional charge quantization, topological degeneracy of the ground states starting from a relatively simple many-body wavefunction, ``root pattern of fractional quantum Hall state. Such an entangled Pauli principle can be derived from a microscopic parent Hamiltonian setting, thereby provide us a potential tool to probe the non-universal physics in quantum Hall fluids as well. Essentially, entangled Pauli principle is the ``DNA of fractional quantum Hall states. Using this guiding principle, we have shown ground states with non-abelian excitations, such as Majorana fermion or Fibonacci fermion can be stabilized for two-particle interaction. Fibonacci fermion supports universal quantum gates, thereby a potential candidate for the topologically protected universal quantum computer. Entangled Pauli principle, along with a recently developed topological order parameter for composite fermions, gives rise to Parent Hamiltonian description for composite fermions as well

Strongly Correlated Systems Under High Magnetic Field: A Mixed Landau Levels Description for Fractional Quantum Hall Effect

Strong correlation among electrons under high magnetic field gives rise to an entirely new arena of emergent physics, namely fractional quantum Hall effect. Such systems have entirely different elementary degrees of freedom and generally, demand non-perturbative approaches to develop a better understanding. In the literature, there are several analytical methodologies and numerical toolkits available to study such a system. Clustering of zeros, parent Hamiltonian, off-diagonal order parameter, parton construction, matrix product states are to be named among a few of those popular methodologies in the existing literature. Most of these methods work well in the lowest Landau level or holomorphic wavefunction framework. It is, however, imperative to develop such methodology to study systems with Landau levels mixing to study more exotic as well as experimentally relevant states. In this work, we have developed particular methodologies, which denounce the traditional importance of the analytic properties of first quantized model wavefunction thereby extend the existing parent Hamiltonian, topological order-parameter, matrix product states descriptions to mixed Landau level systems. Such extension produces a deeper, compact and holistic understanding of universal physics of exotic phases in strongly correlated systems from the microscopic viewpoint, as well as produces interesting new results. Our second quantized/ non-analytic approach allows us to construct the ``entangled Pauli principle , a guidebook to extract universal/topological properties such as braiding statistics, fractional charge quantization, topological degeneracy of the ground states starting from a relatively simple many-body wavefunction, ``root pattern of fractional quantum Hall state. Such an entangled Pauli principle can be derived from a microscopic parent Hamiltonian setting, thereby provide us a potential tool to probe the non-universal physics in quantum Hall fluids as well. Essentially, entangled Pauli principle is the ``DNA of fractional quantum Hall states. Using this guiding principle, we have shown ground states with non-abelian excitations, such as Majorana fermion or Fibonacci fermion can be stabilized for two-particle interaction. Fibonacci fermion supports universal quantum gates, thereby a potential candidate for the topologically protected universal quantum computer. Entangled Pauli principle, along with a recently developed topological order parameter for composite fermions, gives rise to Parent Hamiltonian description for composite fermions as well

Intra-species sequence variability in 28s rRNA gene of Oesophagostomum venulosum isolated from goats of West Bengal, India

AbstractObjectiveTo identify genotypes of Oesophagostmum venulosum (O. venulosum) prevailing in West Bengal, India by comparing variation of nucleotide sequences among 28S rRNA.MethodsPCR amplification of partial segment of 28 S rRNA sequence and analysis of sequence amplified product by single strand conformation polymorphism (SSCP).ResultsTwo distinct conformers among male and female parasites were identified by PCR-SSCP analysis. Sequence analysis among conformers revealed the presence of five single nucleotide polymorphisms (SNP) in codon 64, 66, 86, 125 and 146. Secondary RNA prediction structure showed that out of 5 SNPs, 4 occurred at interior loop of RNA which confirmed evolutionary changes among isolates prevailing in this region.ConclusionsSNPs occured in different isolates of O. venulosum might influence critical changes in rRNA folding pattern which influence evolutionary changes among isolates

CODC: A Copula-based model to identify differential coexpression

Differential coexpression has recently emerged as a new way to establish a fundamental difference in expression pattern among a group of genes between two populations. Earlier methods used some scoring techniques to detect changes in correlation patterns of a gene pair in two conditions. However, modeling differential coexpression by means of finding differences in the dependence structure of the gene pair has hitherto not been carried out. We exploit a copula-based framework to model differential coexpression between gene pairs in two different conditions. The Copula is used to model the dependency between expression profiles of a gene pair. For a gene pair, the distance between two joint distributions produced by copula is served as differential coexpression. We used five pan-cancer TCGA RNA-Seq data to evaluate the model that outperforms the existing state of the art. Moreover, the proposed model can detect a mild change in the coexpression pattern across two conditions. For noisy expression data, the proposed method perf