Spin Chains in an External Magnetic Field. Closure of the Haldane Gap and Effective Field Theories

We investigate both numerically and analytically the behaviour of a spin-1 antiferromagnetic (AFM) isotropic Heisenberg chain in an external magnetic field. Extensive DMRG studies of chains up to N=80 sites extend previous analyses and exhibit the well known phenomenon of the closure of the Haldane gap at a lower critical field H_c1. We obtain an estimate of the gap below H_c1. Above the lower critical field, when the correlation functions exhibit algebraic decay, we obtain the critical exponent as a function of the net magnetization as well as the magnetization curve up to the saturation (upper critical) field H_c2. We argue that, despite the fact that the SO(3) symmetry of the model is explicitly broken by the field, the Haldane phase of the model is still well described by an SO(3) nonlinear sigma-model. A mean-field theory is developed for the latter and its predictions are compared with those of the numerical analysis and with the existing literature.Comment: 11 pages, 4 eps figure

Accurate photoionisation cross section for He at non-resonant photon energies

The total single-photon ionisation cross section was calculated for helium atoms in their ground state. Using a full configuration-interaction approach the photoionisation cross section was extracted from the complex-scaled resolvent. In the energy range from ionisation threshold to 59\,eV our results agree with an earlier $B$-spline based calculation in which the continuum is box discretised within a relative error of $0.01\%$ in the non-resonant part of the spectrum. Above the \He^{++} threshold our results agree on the other hand very well to a recent Floquet calculation. Thus our calculation confirms the previously reported deviations from the experimental reference data outside the claimed error estimate. In order to extend the calculated spectrum to very high energies, an analytical hydrogenic-type model tail is introduced that should become asymptotically exact for infinite photon energies. Its universality is investigated considering also H$^-$, Li$^+$, and HeH$^+$. With the aid of the tail corrections to the dipole approximation are estimated.Comment: 20 pages, 7 figures, 2 table

Long-distance entanglement and quantum teleportation in XX spin chains

Isotropic XX models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We introduce two types of models: I) open, dimerized XX chains, and II) open XX chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model I) supports true long-distance entanglement at zero temperature, while model II) supports {\it ``quasi long-distance''} entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model I) and algebraic in model II), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.Comment: 9 pages, 6 figure

Bures metric over thermal state manifolds and quantum criticality

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows to complement the understanding of the phase diagram including cross-over regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.Comment: 9 pages, 4 figures, LaTeX problems fixed, references adde

State-dependent TMS reveals representation of affective body movements in the anterior intraparietal cortex

In humans, recognition of others’ actions involves a cortical network that comprises, among other cortical regions, the posterior superior temporal sulcus (pSTS), where biological motion is coded and the anterior intraparietal suclus (aIPS), where movement information is elaborated in terms of meaningful goal directed actions. This action observation system (AOS) is thought to encode neutral voluntary actions, and possibly some aspects of affective motor repertoire, but the role of the AOS’ areas in processing affective kinematic information has never been examined. Here we investigated whether the action observation system plays a role in representing dynamic emotional bodily expressions. In the first experiment, we assessed behavioural adaptation effects of observed affective movements. Participants watched series of happy or fearful whole-body point-light displays (PLDs) as adapters and were then asked to perform an explicit categorization of the emotion expressed in test PLDs. Participants were slower when categorizing any of the two emotions as long as it was congruent with the emotion in the adapter sequence. We interpreted this effect as adaptation to the emotional content of PLDs. In the second experiment, we combined this paradigm with TMS applied over either the right aIPS, pSTS and the right half of the occipital pole (corresponding to Brodmann’s area 17 and serving as control) to examine the neural locus of the adaptation effect. TMS over the aIPS (but not over the other sites) reversed the behavioural cost of adaptation, specifically for fearful contents. This demonstrates that aIPS contains an explicit representation of affective body movements

Exact infinite-time statistics of the Loschmidt echo for a quantum quench

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasi-critical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.Comment: 4 pages, 2 figure

Design guidelines for web readability

Reading is fundamental to interactive-system use, but around 800 million of people might struggle with it due to literacy difficulties. Few websites are designed for high readability, as readability remains an underinvestigated facet of User Experience. Existing readability guidelines have multiple issues: they are too many or too generic, poorly worded, and often lack cognitive grounding. This paper developed a set of 61 readability guidelines in a series of workshops with design and dyslexia experts. A user study with dyslexic and average readers further narrowed the 61-guideline set down to a core set of 12 guidelines - an acceptably small set to keep in mind while designing. The core-set guidelines address reformatting - such as using larger fonts and narrower content columns, or avoiding underlining and italics - and may well aply to the interactive system other than websites. © 2017 Copyright is held by the owner/author(s)

Probability density of quantum expectation values

We consider the quantum expectation value \mathcal{A}=\ of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we comment on the relevance of the central limit theorem and draw some results on an alternative statistical mechanics based on the uniform measure on the energy shell.Comment: Substantial revision. References adde

ALTICORE: an initiative for coastal altimetry

ALTICORE (value-added ALTImetry for COastal REgions) is an international initiative whose main objective is to encourage the operational use of altimetry over coastal areas, by improving the quality and availability of coastal altimetry data. The ALTICORE proposal has recently been submitted for funding to the INTAS scheme (www.intas.be) by a consortium of partners from Italy, France, UK, Russia and Azerbaijan. ALTICORE is also meant as a contribution to the ongoing International Altimeter Service effort. In this work we will describe the anticipated project stages, namely: 1) improvement of the most widely distributed, 1 Hz, data by analyzing the corrective terms and providing the best solutions, including those derived from appropriate local modelling; 2) development of a set of algorithms to automate quality control and gap-filling functions for the coastal regions; 3) development of testing strategies to ensure a thorough validation of the data. The improved products will be delivered to ALTICORE users via Grid-compliant technology; this makes it easier to integrate the local data holdings, allows access from a range of services, e.g. directly into model assimilation or GIS systems and should therefore facilitate a widespread and complete assessment of the 1Hz data performance and limitations. We will also outline the design and implementation of the Grid-compliant system for efficient access to distributed archives of data; this consists of regional data centres, each having primary responsibility for regional archives, local corrections and quality control, and operating a set of web-services allowing access to the full functionality of data extraction. We will conclude by discussing a follow-on phase of the project; this will investigate further improvements on the processing strategy, including the use of higher frequency (10 or 20 Hz) data. Phenomena happen at smaller spatial scales near the coast, so this approach is necessary to match the required resolution. The whole project will hopefully promote the 15-year sea surface height from altimetry to the rank of operational record for the coastal areas

Finding critical points using improved scaling Ansaetze

Analyzing in detail the first corrections to the scaling hypothesis, we develop accelerated methods for the determination of critical points from finite size data. The output of these procedures are sequences of pseudo-critical points which rapidly converge towards the true critical points. In fact more rapidly than previously existing methods like the Phenomenological Renormalization Group approach. Our methods are valid in any spatial dimensionality and both for quantum or classical statistical systems. Having at disposal fast converging sequences, allows to draw conclusions on the basis of shorter system sizes, and can be extremely important in particularly hard cases like two-dimensional quantum systems with frustrations or when the sign problem occurs. We test the effectiveness of our methods both analytically on the basis of the one-dimensional XY model, and numerically at phase transitions occurring in non integrable spin models. In particular, we show how a new Homogeneity Condition Method is able to locate the onset of the Berezinskii-Kosterlitz-Thouless transition making only use of ground-state quantities on relatively small systems.Comment: 16 pages, 4 figures. New version including more general Ansaetze basically applicable to all case