Renormalization group approach to symmetry protected topological phases

A defining feature of a symmetry protected topological phase (SPT) in one-dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.Comment: 5 pages, 3 figure

On the Density of Coprime m-tuples over Holomorphy Rings

Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-tuples of polynomials are obtained as corollaries.Comment: To appear in International Journal of Number Theor

Localization dynamics of fluids in random confinement

The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we find delocalized tracer particle dynamics at small matrix area fractions and localized motion of the tracers at high matrix area fractions. In the delocalized region, the dynamics is subdiffusive at intermediate times, and diffusive at long times, while in the localized regime, trapping in finite pockets of the matrix is observed. These observations are found to agree with the simulation of an ideal gas confined in a weakly correlated matrix. Our results show that Lorentz gas systems with soft interactions are exhibiting a smoothening of the critical dynamics and consequently a rounded delocalization-to-localization transition.Comment: 5 pages, 3 figure

Mutual influence of posttraumatic stress disorder symptoms and chronic pain among injured accident survivors: A longitudinal study

The relationship between acute stress disorder (ASD), posttraumatic stress disorder symptoms (PTSD), and chronic pain was investigated in a longitudinal study of injured accident victims (N = 323, 64.7% men). Assessments took place 5 days (T1), 6 (T2) months, and 12 (T3) months postaccident. Relations between pain and posttraumatic stress symptoms were tested by structural equation modeling. Subjects diagnosed with full or subsyndromal PTSD at T2 and at T3 (14 and 19%) reported significantly higher pain intensity. Cross-lagged panel analysis yielded a mutual maintenance of pain intensity and ASD or PTSD symptoms across T2. Across the second half year, PTSD symptoms impacted significantly on pain but not vice versa. Clinicians need to pay careful attention to PTSD symptoms in accident survivors suffering from chronic pain

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and non-topological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing the spin-triplet superfluid 3He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where Green's function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green's function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.Comment: 5 pages, 2 figures, JETP Letters style, version submitted to JETP Letter

Experimental erosion of microbial diversity decreases soil CH4_4 consumption rates

Biodiversity‐ecosystem functioning (BEF) experiments have predominantly focused on communities of higher organisms, in particular plants, with comparably little known to date about the relevance of biodiversity for microbially driven biogeochemical processes. Methanotrophic bacteria play a key role in Earth's methane (CH$_{4}$) cycle by removing atmospheric CH$_{4}$ and reducing emissions from methanogenesis in wetlands and landfills. Here, we used a dilution‐to‐extinction approach to simulate diversity loss in a methanotrophic landfill cover soil community. Replicate samples were diluted 10$^{1}$–10$^{7}$‐fold, preincubated under a high CH$_{4}$ atmosphere for microbial communities to recover to comparable size, and then incubated for 86 days at constant or diurnally cycling temperature. We hypothesize that (1) CH$_{4}$ consumption decreases as methanotrophic diversity is lost, and (2) this effect is more pronounced under variable temperatures. Net CH$_{4}$ consumption was determined by gas chromatography. Microbial community composition was determined by DNA extraction and sequencing of amplicons specific to methanotrophs and bacteria (pmoA and 16S gene fragments). The richness of operational taxonomic units (OTU) of methanotrophic and nonmethanotrophic bacteria decreased approximately linearly with log‐dilution. CH$_{4}$ consumption decreased with the number of OTUs lost, independent of community size. These effects were independent of temperature cycling. The diversity effects we found occured in relatively diverse communities, challenging the notion of high functional redundancy mediating high resistance to diversity erosion in natural microbial systems. The effects also resemble the ones for higher organisms, suggesting that BEF relationships are universal across taxa and spatial scales

Experimental erosion of microbial diversity decreases soil CH4_4 consumption rates

Biodiversity‐ecosystem functioning (BEF) experiments have predominantly focused on communities of higher organisms, in particular plants, with comparably little known to date about the relevance of biodiversity for microbially driven biogeochemical processes. Methanotrophic bacteria play a key role in Earth's methane (CH$_{4}$) cycle by removing atmospheric CH$_{4}$ and reducing emissions from methanogenesis in wetlands and landfills. Here, we used a dilution‐to‐extinction approach to simulate diversity loss in a methanotrophic landfill cover soil community. Replicate samples were diluted 10$^{1}$–10$^{7}$‐fold, preincubated under a high CH$_{4}$ atmosphere for microbial communities to recover to comparable size, and then incubated for 86 days at constant or diurnally cycling temperature. We hypothesize that (1) CH$_{4}$ consumption decreases as methanotrophic diversity is lost, and (2) this effect is more pronounced under variable temperatures. Net CH$_{4}$ consumption was determined by gas chromatography. Microbial community composition was determined by DNA extraction and sequencing of amplicons specific to methanotrophs and bacteria (pmoA and 16S gene fragments). The richness of operational taxonomic units (OTU) of methanotrophic and nonmethanotrophic bacteria decreased approximately linearly with log‐dilution. CH$_{4}$ consumption decreased with the number of OTUs lost, independent of community size. These effects were independent of temperature cycling. The diversity effects we found occured in relatively diverse communities, challenging the notion of high functional redundancy mediating high resistance to diversity erosion in natural microbial systems. The effects also resemble the ones for higher organisms, suggesting that BEF relationships are universal across taxa and spatial scales

Do temporal and spatial heterogeneity modulate biodiversity–functioning relationships in com-munities of methanotrophic bacteria?

Positive relationships between biodiversity functioning have been found in communities of plants but also of soil microbes. The beneficial effects of diversity are thought to be driven by niche partitioning among community members, which leads to more complete or more efficient community-level resource use through various mechanisms. An intriguing related question is whether environmentally more heterogeneous habitats provide a larger total niche space and support stronger diversity—functioning relationships because they harbor more species or allow species to partition the available niche space more efficiently. Here, we tested this hypothesis by assembling communities of 1, 2 or 4 methanotrophic isolates and exposing them to temporally (constant or diurnal temperature cycling) and structurally (one or two aggregate size classes) more heterogeneous conditions. In total, we incubated 396 microcosms for 41 days and found that more biodiverse communities consumed more methane (CH4) and tended to have a larger community size (higher pmoA copy numbers). Diurnal temperature cycling strongly reduced CH4 oxidation and growth, whereas soil aggregate composition and diversity had no detectable effect. Biodiversity effects varied greatly with the identity of the community members that were combined. With respect to community level CH4 consumption, strain interactions were positive or neutral but never negative, and could neither be explained by 14 structural and function traits we collected or by the observed competitive hierarchy among the strains. Overall, our results indicate that methanotrophic diversity promotes methanotrophic community functioning. The strains that performed best varied with environmental conditions, suggesting that a high biodiversity is important for maintaining methanotrophic functioning as environmental conditions fluctuate over time