Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice

We use the non-perturbative Contractor-Renormalization method (CORE) in order to derive an effective model for triplet excitations on the Shastry-Sutherland lattice. For strong enough magnetic fields, various magnetization plateaux are observed, e.g. at 1/8, 1/4, 1/3 of the saturation, as found experimentally in a related compound. Moreover, other stable plateaux are found at 1/9, 1/6 or 2/9. We give a critical review of previous works and try to resolve some apparent inconsistencies between various theoretical approaches.Comment: published version with minor change

Theory of magnetization plateaux in the Shastry-Sutherland model

Using perturbative continuous unitary transformations, we determine the long-range interactions between triplets in the Shastry-Sutherland model, and we show that an unexpected structure develops at low magnetization with plateaux progressively appearing at 2/9, 1/6, 1/9 and 2/15 upon increasing the inter-dimer coupling. A critical comparison with previous approaches is included. Implications for the compound SrCu$_2$(BO$_3$)$_2$ are also discussed: we reproduce the magnetization profile around localized triplets revealed by NMR, we predict the presence of a 1/6 plateau, and we suggest that residual interactions beyond the Shastry-Sutherland model are responsible for the other plateaux below 1/3.Comment: 5 pages, 6 figure

Modelling of crowded polymers elucidate effects of double-strand breaks in topological domains of bacterial chromosomes.

Using numerical simulations of pairs of long polymeric chains confined in microscopic cylinders, we investigate consequences of double-strand DNA breaks occurring in independent topological domains, such as these constituting bacterial chromosomes. Our simulations show a transition between segregated and mixed state upon linearization of one of the modelled topological domains. Our results explain how chromosomal organization into topological domains can fulfil two opposite conditions: (i) effectively repulse various loops from each other thus promoting chromosome separation and (ii) permit local DNA intermingling when one or more loops are broken and need to be repaired in a process that requires homology search between broken ends and their homologous sequences in closely positioned sister chromatid

Die Entwicklung der Vektorrechnung im französischen Mathematikunterricht seit Ende des 19. Jahrhunderts

Zusammenfassung: Dieser Text ist Teil eines größeren Forschungsprojekts über die Verbindungen zwischen Mathematik und Physik und stellt eine Analyse der Geschichte der Vektorrechnung im Unterricht in Frankreich dar, von ihren ersten Anfängen in der Sekundarstufe am Ende des 19 Jhd. bis zur Gegenwart. Unsere Analyse stützt sich auf einen theoretischen Rahmen, der durch die "Oekologie des Wissens" inspiriert ist (Chevallard, 1994). Über das historische Interesse hinaus wollen wir einen Bereich des Mathematikunterrichtes beleuchten (der unter dem Einfluss der jüngsten Reformen immer kleiner und kleiner wird) sowie seinen Bezug zum Physikunterricht, der - obwohl er von beiden Seiten als natürlich angesehen wird - nicht wirklich als effektive Unterstützung der Lehrer der jeweiligen Disziplin zu dienen schein

Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets

We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization respectively. Using Quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove in particular that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.Comment: 4 pages; 4 figures; published versio

Single-particle versus pair condensation of hard-core bosons with correlated hopping

We investigate the consequences of correlated hopping on the ground state properties of hard-core bosons on a square lattice as revealed by extensive exact diagonalizations and quantum Monte Carlo simulations. While for non interacting hard-core bosons the effective attraction induced by the correlated hopping leads to phase separation at low density, we show that a modest nearest-neighbor repulsion suppresses phase separation, leading to a remarkable low-density pairing phase with no single particle Bose-Einstein condensation but long-range two-particle correlations, signaling a condensation of pairs. We also explain why the unusual properties of the pairing phase are a real challenge for standard one-worm quantum Monte Carlo simulations.Comment: 8 pages, 7 figure

Effects of supercoiling on enhancer-promoter contacts.

Using Brownian dynamics simulations, we investigate here one of possible roles of supercoiling within topological domains constituting interphase chromosomes of higher eukaryotes. We analysed how supercoiling affects the interaction between enhancers and promoters that are located in the same or in neighbouring topological domains. We show here that enhancer-promoter affinity and supercoiling act synergistically in increasing the fraction of time during which enhancer and promoter stay in contact. This stabilizing effect of supercoiling only acts on enhancers and promoters located in the same topological domain. We propose that the primary role of recently observed supercoiling of topological domains in interphase chromosomes of higher eukaryotes is to assure that enhancers contact almost exclusively their cognate promoters located in the same topological domain and avoid contacts with very similar promoters but located in neighbouring topological domains

Magnetization plateaux in an extended Shastry-Sutherland model

We study an extended two-dimensional Shastry-Sutherland model in a magnetic field where besides the usual Heisenberg exchanges of the Shastry-Sutherland model two additional SU(2) invariant couplings are included. Perturbative continous unitary transformations are used to determine the leading order effects of the additional couplings on the pure hopping and on the long-range interactions between the triplons which are the most relevant terms for small magnetization. We then compare the energy of various magnetization plateaux in the classical limit and we discuss the implications for the two-dimensional quantum magnet SrCu$_2$(BO$_3$)$_2$.Comment: 8 pages, Proceedings of the HFM2008 Conferenc

Transcription-induced supercoiling as the driving force of chromatin loop extrusion during formation of TADs in interphase chromosomes.

Using molecular dynamics simulations, we show here that growing plectonemes resulting from transcription-induced supercoiling have the ability to actively push cohesin rings along chromatin fibres. The pushing direction is such that within each topologically associating domain (TAD) cohesin rings forming handcuffs move from the source of supercoiling, constituted by RNA polymerase with associated DNA topoisomerase TOP1, towards borders of TADs, where supercoiling is released by topoisomerase TOPIIB. Cohesin handcuffs are pushed by continuous flux of supercoiling that is generated by transcription and is then progressively released by action of TOPIIB located at TADs borders. Our model explains what can be the driving force of chromatin loop extrusion and how it can be ensured that loops grow quickly and in a good direction. In addition, the supercoiling-driven loop extrusion mechanism is consistent with earlier explanations proposing why TADs flanked by convergent CTCF binding sites form more stable chromatin loops than TADs flanked by divergent CTCF binding sites. We discuss the role of supercoiling in stimulating enhancer promoter contacts and propose that transcription of eRNA sends the first wave of supercoiling that can activate mRNA transcription in a given TAD