Bond-ordered states and ff-wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.Comment: 11 pages, 11 figure

The Jacobson Radical of a Propositional Theory

Alongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum's Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko's Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style entailment relation over a single-conclusion one.Peer reviewe

Unterstützung von Interesse und Wissensaustausch mittels mobiler Geräte und Bookmarking in Wissenschafts- und Technologie-Museen

Why are some exhibits interesting for a particular visitor? Is it possible to support this elicited interest during the museum visit with mobile devices that offer additional information or with the information that is available in the museum on the spot? Is it possible to support interest after the museum visit when visitors are able to bookmark the information that they personally found interesting during their visit and to view this information on a personal webpage after the visit? These three questions are addressed in the two studies of the present dissertation thesis in the context of science and technology museums. The first study was conducted in a laboratory exhibition about nanotechnology with 62 student participants and the two factors “availability of additional information” and “availability of bookmarking” on a mobile device. Availability of additional information had a strong effect on visit duration as a behavioral indicator of interest, but no effect on self-reported interest or knowledge measures. However, visitors with additional information reported more post-visit involvement with the topic, possibly indicating a “foot-in-the-door” effect of additional information. Bookmarking did not show an effect, as the exhibition webpage was rarely used. To alleviate constraints with paid student participants, a second study with higher ecological validity was conducted in an actual museum. The sample comprised 188 regular visitors, with the experimental group (n = 75) having immediate access to all exhibition information on the mobile device and being able to bookmark information, while the control group (n = 113) visited the museum unassisted. An exploratory factor analysis (PAF, varimax) led to the identification of four factors in the visitor-exhibit relationship that determine whether a particular exhibit is interesting for a particular visitor: Attraction Power, Instant Enjoyment, Familiarity, and Information Value. These four factors can explain why interactive and the by far largest exhibit is mentioned more frequently as the most interesting exhibit than their occurrence in the museum would suggest. The four factors can also explain subjective theories of museum curators and the theories of museum professionals regarding interesting exhibits. A strong effect of the device was found for visit duration, but not for self-reported interest and knowledge. Bookmarking was rarely used by the experimental group. The influence of the device can be explained by Rounds’ (2004) application of information foraging to the museum context if this theory is augmented by the effects of using a mobile device in the museum. Adding a virtual information space on a mobile device on top of the information space of the physical museum can enlarge the interest landscape for the museum visitor (Study 1) and support the visitor in exploring it (Study 2). This has beneficial consequences for visitor behavior — information is accessed, and visitors spend more time in the exhibition using the device before museum fatigue sets in, while self-reports show no difference as they were assessed after the visit (where interest has reached the same level for all conditions). Consequently, mobile devices can be used to support visitors’ interest. While bookmarking is used by some visitors, no effects could be found, as museum visit wrap-ups by visitors were rare. Visitor motivation for museum visit wrap-ups must be supported first before bookmarking can have any effect.Warum sind einige Ausstellungsstücke interessant für bestimmte Besucher? Ist es möglich, in Ausstellungen auftretendes Interesse mit mobilen Geräten zu unterstützen, die Zusatzinformationen zur Verfügung stellen oder die im Museum verfügbaren Informationen an Ort und Stelle verfügbar machen? Ist es möglich, nach dem Ausstellungsbesuch Interesse zu unterstützen, wenn Besucher interessante Informationen während des Besuches speichern können und diese nach dem Besuch auf einer persönlichen Webseite ansehen können? Diese drei Fragen werden in dieser Dissertation bezüglich Wissenschafts- und Technologiemuseen in zwei Studien untersucht. Die erste Studie wurde in einer Laborausstellung über Nanotechnologie mit 62 studentischen Versuchspersonen mit den Faktoren “Verfügbarkeit von Zusatzinformationen” und “Verfügbarkeit von Bookmarking” auf einem mobilen Gerät durchgeführt. Verfügbarkeit von Zusatzinformationen hatte einen starken Effekt auf einen Verhaltensindikator von Interesse, Dauer des Besuches, aber keinen Effekt auf die selbstberichteten Interessens- oder Wissensmaße. Besucher mit Zusatzinformationen berichteten allerdings über eine höhere Beschäftigung mit dem Thema nach dem Besuch, was möglicherweise auf einen “Fuß-in-der-Tür”-Effekt von Zusatzinformationen hinweist. Bookmarking zeigte keinen Effekt aufgrund der seltenen Nutzung der Ausstellungswebsite. Um die Beschränkungen von entlohnten studentischen Versuchspersonen aufzuheben, wurde eine zweite Studie mit höherer ökologischer Validität durchgeführt. Die zweite Studie wurde als Feldstudie in einem realen Museum mit 188 normalen Besuchern durchgeführt. Die Experimentalgruppe (n =75) hatte sofortigen Zugang zu allen Ausstellungsinformationen auf dem mobilen Gerät und konnte Informationen speichern, während die Kontrollgruppe (n = 113) das Museum ohne technische Unterstützung besuchte. Eine exploratorische Faktorenanalyse (PAF, Varimax) wurde durchgeführt, welche zur Identifikation von vier Faktoren in der Besucher-Ausstellungsstück-Beziehung führte, die bestimmen, ob ein bestimmtes Ausstellungsstück für einen bestimmten Besucher interessant ist: Anziehungskraft, Sofortiges Vergnügen, Vertrautheit, und Informationswert. Diese vier Faktoren können erklären, warum interaktive und das mit Abstand größte Exponat überzufällig häufig als interessantestes Ausstellungsstück genannt werden. Sie können auch die subjektiven Theorien von Kuratoren und die Theorien von Museumsforscher bezüglich interessanter Exponate erklären. Ein starker Effekt des Gerätes auf die Besuchsdauer wurde gefunden, allerdings nicht für die selbstberichteten Interessens- und Wissensmaße. Bookmarking wurde von der Experimentalgruppe selten verwendet. Der Einfluss des Gerätes kann erklärt werden, wenn man die von Rounds (2004) auf Museumskontexte angewendete “Information Foraging Theory” um die Effekte von mobilen Geräten im Museum erweitert: Wenn ein virtueller Informationsraum mit einem mobilen Gerät über den Informationsraum des physischen Museums aufgespannt wird, kann dies die Interessenlandschaft für den Museumsbesucher erweitern (Studie 1) und dem Besucher die Exploration der Interessenlandschaft des Museums erleichtern (Studie 2). Dies hat positive Konsequenzen für das Besucherverhalten — die Information wird abgerufen und die Besucher verbringen mehr Zeit in der Ausstellung mit dem Gerät, bevor Museumsmüdigkeit auftritt, während die Selbstberichte keine Unterschiede aufweisen, denn sie wurden nach dem Besuch erfasst (als das Interesse für alle Besucher wieder die gleiche Stärke erreicht hat). Entsprechend können mobile Geräte genutzt werden, um das Interesse von Besuchern zu unterstützen. Obwohl Bookmarking von einigen Besuchern verwendet wurde, konnten diesbezüglich keine Effekte gefunden werden, da eine Nachbereitung von Museumsbesuchen sehr selten ist. Die Motivation der Besucher, den Besuch eines Museums nachzubereiten, muss zuerst erhöht werden, bevor Bookmarking einen Einfluss aufweisen kann

Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation

The magnetic properties of graphene on finite geometries are studied using a self-consistent mean-field theory of the Hubbard model. This approach is known to predict ferromagnetic edge states close to the zig-zag edges in single-layer graphene quantum dots and nanoribbons. In order to assess the accuracy of this method, we perform complementary exact diagonalization and quantum Monte Carlo simulations. We observe good quantitative agreement for all quantities investigated provided that the Coulomb interaction is not too strong.Comment: 5 pages including 3 figures; v3: error concerning middle panel of Fig. 3 correcte

Control Improvisation

We formalize and analyze a new automata-theoretic problem termed control improvisation. Given an automaton, the problem is to produce an improviser, a probabilistic algorithm that randomly generates words in its language, subject to two additional constraints: the satisfaction of an admissibility predicate, and the exhibition of a specified amount of randomness. Control improvisation has multiple applications, including, for example, generating musical improvisations that satisfy rhythmic and melodic constraints, where admissibility is determined by some bounded divergence from a reference melody. We analyze the complexity of the control improvisation problem, giving cases where it is efficiently solvable and cases where it is #P-hard or undecidable. We also show how symbolic techniques based on Boolean satisfiability (SAT) solvers can be used to approximately solve some of the intractable cases

Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PD) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD calculations, we obtain exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.Comment: 5+5 pages, 4+4 figure

The art of simulating the early Universe -- Part I

We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of $O(dt^2)$ accuracy like $staggered~leapfrog$ and $Verlet$ integration, to $Runge-Kutta$ methods up to $O(dt^4)$ accuracy, and the $Yoshida$ and $Gauss-Legendre$ higher-order integrators, accurate up to $O(dt^{10})$. We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in $3+1$ dimensions, including the case of `self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: $i)$ Interacting scalar fields, $ii)$ Abelian $U(1)$ gauge theories, and $iii)$ Non-Abelian $SU(2)$ gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from $O(dt^2)$ up to $O(dt^{10})$. For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. Remarkably, all our algorithms for gauge theories respect the Gauss constraint to machine precision, including when `self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under $SU(2)\times U(1)$. The present manuscript is meant as part of the theoretical basis for $CosmoLattice$, a modern C++ MPI-based package for simulating the non-linear dynamics of scalar-gauge field theories in an expanding universe, publicly available at www.cosmolattice.netComment: Minor corrections to match published version, and one more algorithm added. Still 79 pages, 8 figures, 1 appendix, and many algorithm

CosmoLattice

This is the user manual for CosmoLattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoLattice incorporates a series of features that makes it very versatile and powerful: $i)$ it is written in C++ fully exploiting the object oriented programming paradigm, with a modular structure and a clear separation between the physics and the technical details, $ii)$ it is MPI-based and uses a discrete Fourier transform parallelized in multiple spatial dimensions, which makes it specially appropriate for probing scenarios with well-separated scales, running very high resolution simulations, or simply very long ones, $iii)$ it introduces its own symbolic language, defining field variables and operations over them, so that one can introduce differential equations and operators in a manner as close as possible to the continuum, $iv)$ it includes a library of numerical algorithms, ranging from $O(\delta t^2)$ to $O(\delta t^{10})$ methods, suitable for simulating global and gauge theories in an expanding grid, including the case of `self-consistent' expansion sourced by the fields themselves. Relevant observables are provided for each algorithm (e.g.~energy densities, field spectra, lattice snapshots) and we note that remarkably all our algorithms for gauge theories always respect the Gauss constraint to machine precision. In this manual we explain how to obtain and run CosmoLattice in a computer (let it be your laptop, desktop or a cluster). We introduce the general structure of the code and describe in detail the basic files that any user needs to handle. We explain how to implement any model characterized by a scalar potential and a set of scalar fields, either singlets or interacting with $U(1)$ and/or $SU(2)$ gauge fields. CosmoLattice is publicly available at www.cosmolattice.net.Comment: 111 pages, 3 figures and O(100) code file

Courtship behaviour and vibrational communication of the planthopper Apartus michalki (Wagner, 1948): (Hemiptera: Fulgoromorpha: Cixiidae)

Paarungsverhalten und Vibrationskommunikation von Apartus michalki (Wagner, 1948) (Hemiptera: Fulgoromorpha: Cixiidae). – Cixiidae benötigen, wie alle sich sexuell reprodu- zierende Taxa, eine Reihe von Erkennungsmerkmalen, um potentielle Paarungspartner zu identifizieren und zu lokalisieren (specific mate recognition system = SMRS). Zwar ist der Einsatz von akustischen und/oder substratgebundenen Signalen als Teil des SMRS bei Hemipteren bekannt und weit verbreitet, die Kenntnisse zum Paarungsverhalten bei Cixiiden sind jedoch noch lückenhaft. In diesem Beitrag dokumentieren wir zum ersten Mal die Vibrationskommunikation bei Apartus michalki zusammen mit weiteren Beobachtungen zum Paarungsverhalten dieser Art.Cixiidae require a set of clues in order to recognize and localize potential conspecific partners for mating (specific mate recognition system = SMRS). The use of acoustic and/or vibrational signals as part of the SMRS is ubiquitous in Hemiptera. However, the general knowledge of the mating behaviour of Cixiidae is still patchy. Here we report for the first time evidence for vibrational communication in Apartus michalki along with observations of the courtship behaviour