In this paper, we study the ground-state quantum Fisher information (QFI) in one-dimensional spin-1 models, as witness to multipartite entanglement. The models addressed are the bilinear-biquadratic model, the most general isotropic SU(2)-invariant spin-1 chain, and the XXZ spin-1 chain, both with nearest-neighbor interactions and open boundary conditions. We show that the scaling of the QFI of strictly nonlocal observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases, where it scales maximally. Analyzing its behavior at the critical phases, we are also able to recover the scaling dimensions of the order parameters, both for local and string observables. The numerical results have been obtained by exploiting the density-matrix renormalization-group algorithm and tensor network techniques.

We present the prospects of detecting quantum entanglement and the violation of Bell inequalities in t bar{t} events at the LHC. We introduce a unique set of observables suitable for both measurements, and then perform the corresponding analyses using simulated events in the dilepton final state, reconstructing up to the unfolded level. We find that entanglement can be established at better than 5? both at threshold as well as at high pT already in the LHC Run 2 dataset. On the other hand, only very high-pT events are sensitive to a violation of Bell inequalities, making it significantly harder to observe experimentally. By employing a sensitive and robust observable, two different unfolding methods and independent statistical approaches, we conclude that, at variance with previous estimates, testing Bell inequalities will be challenging even in the high luminosity LHC run.

We present computational results associated with the onset of a spin-dependent optical force component occurring on zinc oxide nanowires trapped in optical tweezers with circularly polarized light. This type of non-conservative force appears directed perpendicularly with respect to the propagation direction of the incident light on the nanowires both for plane wave illumination and for optical tweezers. We show how this transverse optical force component is also shape dependent and connected with the imaginary part of the local Poynting vector and the local spin density.

We address the precision of the estimation procedures for the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation performance. At first, we review the concept of minimum length and how it induces a perturbative term appearing in the Hamiltonian of any quantum system, which itself is proportional to a parameter depending on the minimum length. We then systematically study the effects of this perturbation on different state preparations and for several one-dimensional systems, and evaluate the quantum Fisher information in order to find the ultimate bounds to precision. Eventually, we investigate the role of dimensionality by analyzing the use of two-dimensional square well and harmonic oscillator systems to probe the minimal length. Our results show that quantum probes are convenient resources, providing potential enhancement in precision. Additionally, our results provide a set of guidelines to design future experiments to detect the minimum length.

We analyze the possible existence of topological phases in two-legged spin ladders, considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a nonlinear sigma model NL?M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity, and string nonlocal order parameters, correlation functions between x,y,z components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum, and the entanglement entropy to characterize these two different phases. We identify one phase with a Mott insulator and the other one with a Haldane insulator.

We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a nonlinear sigma model plus with a so-called topological term which is nonvanishing even if the number of legs is two. This suggests a quantum phase transition that is explored numerically, using a DMRG approach, by considering energy gaps, surface correlations as well as nonlocal correlators and entanglement indicators such as entropy and degeneracy of reduced density matrix levels. This characterisation indicates the appearance of a topological phase (an analogue of Mott-Haldane transition) with genuine multipartite entanglement, and provide insights in the role of topological field-theoretic terms vs topological states in quasi 1d quantum systems.

Saggio divulgativo sull'utilizzo del concetto di entropia nella comunicazione secondo le idee di Claude Shannon. Parte di: "Entropia - Un affascinante viaggio tra ordine e disordine", a cura di W. Bruno.

Optical tweezers are a crucial tool for the manipulation and characterisation, without mechanical contact, of micro- and nanoparticles, ranging from biological components, such as biomolecules, viruses, bacteria, and cells, to nanotubes, nanowires, layered materials, plasmonic nanoparticles, and their composites. Despite the many interdisciplinary applications, only recently it has been possible to develop an accurate theoretical modelling for the mesoscale size range. This goes beyond the strong approximations typically used for the calculation of optical forces on particles much smaller (dipole approximation) or much larger (ray optics) than the wavelength of the trapping light. Among the different methods used to calculate optical forces on model particles, the ones based on the transition matrix (T-matrix) are currently among the most accurate and efficient, particularly when applied to non-spherical particles, both isolated and interacting, or in composite structures. Here, we first give an overview of the theoretical background on optical forces, optomechanics, and T-matrix methods. Then, we focus on calculations of optical trapping on model polystyrene nanowires with the aim to investigate their scaling with nanowire length at the mesoscale. We compare the force constant dependence with approximations at small or large length with respect to the trapping wavelength and with calculations on spheres, pointing out the role of shape.

Optical tweezers, tools based on strongly focused light, enable optical trapping, manipulation, and characterisation of a wide range of microscopic and nanoscopic materials. In the limiting cases of spherical particles either much smaller or much larger than the trapping wavelength, the force in optical tweezers separates into a conservative gradient force, which is proportional to the light intensity gradient and responsible for trapping, and a non-conservative scattering force, which is proportional to the light intensity and is generally detrimental for trapping, but fundamental for optical manipulation and laser cooling. For non-spherical particles or at intermediate (meso)scales, the situation is more complex and this traditional identification of gradient and scattering force is more elusive. Moreover, shape and composition can have dramatic consequences for optically trapped particle dynamics. Here, after an introduction to the theory and practice of optical forces with a focus on the role of shape and composition, we give an overview of some recent applications to biology, nanotechnology, spectroscopy, stochastic thermodynamics, critical Casimir forces, and active matter.

The Mott insulating state of the Hubbard model at half filling could be depicted as a spin liquid of singly occupied sites with holon-doublon quantum fluctuations localized in pairs. In one dimension the behavior is captured by a finite value of the charge parity string correlator, which fails to remain finite when generalized to higher dimensions. We recover a definition of parity brane correlator which may remain nonvanishing in the presence of interchain coupling, by assigning an appropriate fractional phase to the parity breaking fluctuations. In the case of Hubbard ladders at half filling, we find that the charge parity brane is nonzero at any repulsive value of interaction. The spin-parity brane instead becomes nonvanishing in the even-leg case, in correspondence to the onset of the spin gapped D-Mott phase, which is absent in the odd-leg case. The behavior of the parity correlators is also analyzed by means of a numerical DMRG analysis of the one- and two-leg ladder.

The analysis of the response in transmission electron microscopy, and in particular in electron holography depends ultimately on the electromagnetic field experienced by the electron beam within the sample. However dealing with nanostructures it is not always clear how to relate quantitatively the observed response to the average value of the inner potential integrated across the sample thickness. The Density Functional Theory (DFT) approach provides a set of numerical tools to compute various properties of bulk and nanoscopic materials; specifically, the set of Kohn-Sham equations yields a self-consistent and complete estimate of the inner potential experienced by the electrons. By retaining a sufficient number of basis elements, one can quantify the inner potential and density fields with a sub-angstrom resolution. However the actual possibility of carrying out an analysis of this type is limited by three factors: (a) in a plane-wave setting the infinitely extended directions are easily treated but for the spatially limited ones a supercell scheme is needed; (b) one has to adopt a suitable transferable form of the exchange-correlation terms and associated pseudopotential; (c) the total number of atoms in a unit supercell is necessarily limited by computational resources, ranging from hundreds to a few thousands with current high-performance parellel machines. In this contribution we perform a systematic study of aspects related to (a) and (b), on flat multilayer graphene sheets with up to ten layers, in different stacking configurations [1], employing different proposals of van der Waals exchange-correlation schemes [2,3], to check how the binding energies, interlayer distances, vacuum fields and integrated profiles compare to experimental data. In these cases the approach is fully of DFT nature, meaning that first the nanostructures are relaxed towards minum energy configurations and then the self-consistent fields are post-processed to give the desired response. The resulting dependence on the layers separation and number provides an estimate of a surface- and an interlayer term to be taken as references values in holographic experiments, especially close to folded edges where the layers distance locally increases. Moreover it is seen that the dependence on the relative orientation is weak, probably below the current experimental reach. As far as point (c) is concerned, we have extended and tested the method above using an effective two-stage strategy. When the number of atoms is prohibitively large for a full DFT relaxation, the optimal configurations are first determined by means of a molecular dynamics approach using suitable force fields that yield practically the same shapes as with DFT for samples where the data are available. The larger structures we are interested in [4] are both multilayer folded graphene membranes and large squeezed chiral nanotubes that can be viewed also as folded graphene sheets with chiral folding axis. Once the optimal configuration is available from the first stage the inner charge and potential field can be extracted fully at the quantum level in a final self-consistent "snapshot", allowing for a quantitative numerical counterpart to be compared with microscopy findings. [1] J. M. B. Lopes dos Santos et al., Phys. Rev. Lett. 99 (2007), 256802 [2] S. Grimme, J. Comp. Chem. 27 (2006), 1787 [3] K. Lee et al., Phys. Rev. B 82 (2010), 081101R [4] V. Morandi et al., Topics in Current Chemistry 348 (2014), 205

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 is sequences of pseudo-critical points which rapidly converge towards the true critical points. The convergence is faster than that obtained with the fastest method available to date, which consists of estimating the location of the gap's closure (the so called phenomenological renormalization group). Having fast converging sequences at our disposal allows us to draw conclusions on the basis of shorter system sizes. This can be extremely important in particularly hard cases such as two-dimensional quantum systems with frustrations, or in Monte Carlo simulations when the sign problem occurs. After reviewing the most efficient techniques available to date, we test the effectiveness of the proposed 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 produce fast converging sequences in correspondence to the Berezinskii-Kosterlitz-Thouless (BKT) transition simply by making use of ground-state quantities on relatively small systems. Remarkably, our method tested on the frustrated spin-1/2 Heisenberg model gives a BKT critical point which is incompatible with the ones present in the past literature based on different methods. This discrepancy raises the fundamental question of determining the correct renormalization group approach and scaling assumptions that yield to the sequences converging to the true critical point. Finally, we formulate a general prescription that allows us to analyze and efficiently locate critical points in a variety of cases, without knowing in advance the universality class of the tested transition. Even if our methods are tested here in one dimension, we expect them to be valid in any spatial dimensionality and both for quantum and classical statistical systems.

In the study of quantum properties of many-body interacting systems to ideal extremes may be represented by Density Functional Theory (DFT) on the one side and by Hubbard- or Heisenberg- like models on the other side, the former being a widely used framework for quantitative calculations in realistic materials with moderate correlations and the latter being a route to investigate the role of strong correlations at the price of focusing mainly on universal or qualitative features. A celebrated computational method in this second case is the so-called Density Matrix Renormalization Group (DMRG). During the training worskhop on application porting to the GRID the use case of a popular DFT parallel code - Quantum Espresso - was presented. There is evidence that for systems with tens of atoms and periodic boundary conditions or for problems in which the computational load can be splitted in an almost parallel way, such as the calculation of the entries of a vibrational dynamic matrix, the GRID approach proves to be successful. However, when the number of atoms reaches O(100) a massively parallel treatment is required and the overall performance of the GRID approach may be significantly affected by intercommunication latencies and priority policies. On the DMRG side, instead, the execution is typically serial but an advantageous use of the GRID may be the istance of many independent runs for different system's parameters. For example, using the DIRAC submission tool within portal.italiangrid.it we could collect thousands of runs to compute the ground-state entanglement entropy of a class of spin-1 quantum Hamiltonians with spatial anisotropy, whose phase diagram is still controversial in some parts.

The expansion dynamics of bosonic gases in optical lattices has recently been the focus of increasing attention, both experimental and theoretical. We consider, by means of numerical Bethe ansatz, the expansion dynamics of initially confined wave packets of two interacting bosons on a lattice. We show that a correspondence between the asymptotic expansion velocities and the projection of the evolved wave function over the bound states of the system exists, clarifying the existing picture for such situations. Moreover, we investigate the role of the lattice in this kind of evolution.

The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations.

We numerically determine the very rich phase diagram of mass-imbalanced binary mixtures of hardcore bosons (or equivalently - fermions, or hardcore Bose/Fermi mixtures) loaded in one-dimensional optical lattices. Focusing on commensurate fillings away from half-filling, we find a strong asymmetry between attractive and repulsive interactions. Attraction is found to always lead to pairing, associated with a spin gap, and to pair crystallization for very strong mass imbalance. In the repulsive case the two atomic components remain instead fully gapless over a large parameter range; only a very strong mass imbalance leads to the opening of a spin gap. The spin-gap phase is the precursor of a crystalline phase occurring for an even stronger mass imbalance. The fundamental asymmetry of the phase diagram is at odds with recent theoretical predictions, and can be tested directly via time-of-flight experiments on trapped cold atoms. © 2012 Europhysics Letters Association.