Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes

Disorder is ubiquitous in solid-state systems, and its crucial influence on transport properties was revealed by the discovery of Anderson localization. Generally speaking, all bulk states will be exponentially localized in the strong disorder limit, but whether an Anderson transition takes place depends on the dimension and symmetries of the system. The scaling theory and symmetry classes are at the heart of the study of the Anderson transition, and the critical exponent $\nu$ characterizing the power-law divergence of localization length is of particular interest. In contrast with the well-established lower critical dimension $d_l=2$ of the Anderson transition, the upper critical dimension $d_u$, above which the disordered system can be described by mean-field theory, remains uncertain, and precise numerical evaluations of the critical exponent in higher dimensions are needed. In this study, we apply Borel-Pad\'e resummation method to the known perturbative results of the non-linear sigma model (NL$\sigma$M) to estimate the critical exponents of the Boguliubov-de Gennes (BdG) classes. We also report numerical simulations of class DIII in 3D, and classes C and CI in 4D, and compare the results of the resummation method with these and previously published work. Our results may be experimentally tested in realizations of quantum kicked rotor models in atomic-optic systems, where the critical behavior of dynamical localization in higher dimensions can be measured.Comment: 11 pages, 6 figure

Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition

Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. In this letter, we employ large-scale density matrix renormalization group simulations to investigate the critical spin chain with long-range interaction $V(r) \sim 1/r^{\alpha}$. Remarkably, we reveal that the long-range interaction drives the deconfined criticality towards a first-order phase transition as $\alpha$ decreases. More strikingly, the emergent self-duality leads to an emergent symmetry and manifests at these first-order critical points. This discovery is reminiscent of self-duality protected multicritical points and provides the example of the critical line with generalized symmetry. Our work has far-reaching implications for ongoing experimental efforts in Rydberg atom quantum simulators.Comment: 5 + 10 pages, 9 figures. Any comments or suggestions are welcome

Identification and Discrimination of Salmonella enterica Serovar Gallinarum Biovars Pullorum and Gallinarum Based on a One-Step Multiplex PCR Assay

Salmonella enterica serovar Gallinarum biovars Pullorum (S. Pullorum) and Gallinarum (S. Gallinarum) can result in pullorum disease and fowl typhoid in avian species, respectively, and cause considerable economic losses in poultry in many developing countries. Conventional Salmonella serotyping is a time-consuming, labor-intensive and expensive process, and the two biovars cannot be distinguished using the traditional serological method. In this study, we developed a rapid and reliable one-step multiplex polymerase chain reaction (PCR) assay to simultaneously identify and discriminate the biovars Pullorum and Gallinarum. The multiplex PCR method focused on three specific genes, stn, I137_08605 and ratA. Based on bioinformatics analysis, we found that gene I137_08605 was present only in S. Pullorum and S. Gallinarum, and a region of difference in ratA was deleted only in S. Pullorum after comparison with that of S. Gallinarum and other Salmonella serovars. Three pairs of primers specific for the three genes were designed for the multiplex PCR system and their selectivity and sensitivity were determined. The multiplex PCR results showed that S. Pullorum and S. Gallinarum could be identified and discriminated accurately from all tested strains including 124 strains of various Salmonella serovars and 42 strains of different non-Salmonella pathogens. In addition, this multiplex PCR assay could detect a minimum genomic DNA concentration of 67.4 pg/μL, and 100 colony forming units. The efficiency of the multiplex PCR was evaluated by detecting natural-occurring Salmonella isolates from a chicken farm. The results demonstrated that the established multiplex PCR was able to identify S. Gallinarum and S. Pullorum individually, with results being consistent with traditional serotyping and biochemical testing. These results demonstrated that a highly accurate and simple biovar-specific multiplex PCR assay could be performed for the rapid identification and discrimination of Salmonella biovars Gallinarum and Pullorum, which will be useful, particularly under massive screening situations