Quantum phase transitions occur at zero temperature and involve the appearance of long-range correlations. These correlations are not due to thermal fluctuations but to the intricate structure of a strongly entangled ground state of the system. We present a microscopic computation of the scaling properties of the ground-state entanglement in several 1D spin chain models both near and at the quantum critical regimes. We quantify entanglement by using the entropy of the ground state when the system is traced down to L spins. This entropy is seen to scale logarithmically with L, with a coefficient that corresponds to the central charge associated to the conformal theory that describes the universal properties of the quantum phase transition. Thus we show that entanglement, a key concept of quantum information science, obeys universal scaling laws as dictated by the representations of the conformal group and its classification motivated by string theory. This connection unveils a monotonicity law for ground-state entanglement along the renormalization group flow. We also identify a majorization rule possibly associated to conformal invariance and apply the present results to interpret the breakdown of density matrix renormalization group techniques near a critical point. The study of entanglement in composite systems is one of the major goals of quantum information science [1,2], where entangled states are regarded as a valuable resource for processing information in novel ways. For instance, the entanglement between systems A and B in a joint pure state |Ψ AB can be used, together with a classical channel, to teleport or send quantum information [3]. From this resource-oriented perspective, the entropy of entanglement E(Ψ AB ) measures the entanglement contained in |Ψ AB [4]. It is defined as the von Neumann entropy of the reduced density matrix ρ A (equivalently ρ B ),and directly determines, among other aspects, how much quantum information can be teleported by using |Ψ AB . On the other hand, entanglement is appointed to play a central role in the study of strongly correlated quantum systems [5,6,7], since a highly entangled ground state is at the heart of a large variety of collective quantum phenomena. Milestone examples are the entangled ground states used to explain superconductivity and the fractional quantum Hall effect, namely the BCS ansatz [8] and the Laughlin ansatz [9]. Ground-state entanglement is, most promisingly, also a key factor to understand quantum phase transitions [10,11], where it is directly responsible for the appearance of long-range correlations. Consequently, a gain of insight into phenomena including, among others, Mott insulator-superfluid transitions, quantum magnet-paramagnet transitions and phase transitions in a Fermi liquid is expected by studying the structure of entanglement in the corresponding underlying ground states.In the following we analyze the ground-state entanglement near and at a quantum critical point in a series of 1D spin-1/2 chain models. In particular, we consi...

We present NNPDF3.0, the first set of parton distribution functions (PDFs) determined with a methodology validated by a closure test. NNPDF3.0 uses a global dataset including HERA-II deep-inelastic inclusive cross-sections, the combined HERA charm data, jet production from ATLAS and CMS, vector boson rapidity and transverse momentum distributions from ATLAS, CMS and LHCb, W +c data from CMS and top quark pair production total cross sections from ATLAS and CMS. Results are based on LO, NLO and NNLO QCD theory and also include electroweak corrections. To validate our methodology, we show that PDFs determined from pseudo-data generated from a known underlying law correctly reproduce the statistical distributions expected on the basis of JHEP04(2015)040the assumed experimental uncertainties. This closure test ensures that our methodological uncertainties are negligible in comparison to the generic theoretical and experimental uncertainties of PDF determination. This enables us to determine with confidence PDFs at different perturbative orders and using a variety of experimental datasets ranging from HERA-only up to a global set including the latest LHC results, all using precisely the same validated methodology. We explore some of the phenomenological implications of our results for the upcoming 13 TeV Run of the LHC, in particular for Higgs production cross-sections.

We present the first determination of parton distributions of the nucleon at NLO and NNLO based on a global data set which includes LHC data: NNPDF2.3. Our data set includes, besides the deep inelastic, Drell-Yan, gauge boson production and jet data already used in previous global PDF determinations, all the relevant LHC data for which experimental systematic uncertainties are currently available: ATLAS and LHCb W and Z rapidity distributions from the 2010 run, CMS W electron asymmetry data from the 2011 run, and ATLAS inclusive jet cross-sections from the 2010 run. We introduce an improved implementation of the FastKernel method which allows us to fit to this extended data set, and also to adopt a more effective minimization methodology. We present the NNPDF2.3 PDF sets, and compare them to the NNPDF2.1 sets to assess the impact of the LHC data. We find that all the LHC data are broadly consistent with each other and with all the older data sets included in the fit. We present predictions for various standard candle cross-sections, and compare them to those obtained previously using NNPDF2.1, and specifically discuss the impact of ATLAS electroweak data on the determination of the strangeness fraction of the proton. We also present collider PDF sets, constructed using only data from HERA, Tevatron and LHC, but find that this data set is neither precise nor complete enough for a competitive PDF determination.

We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light-quark and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and Z production in the forward region at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. We also include for the first time top-quark pair differential distributions and the transverse momentum of the Z bosons from ATLAS and CMS. We investigate the impact of parametrizing charm and provide evidence that the accuracy and stability of the PDFs are thereby improved. We study the impact of the new data by producing a variety of determinations based on reduced datasets. We find that both improvements have a significant impact on the PDFs, with some substantial reductions in uncertainties, but with the new PDFs generally in agreement with the previous set at the one-sigma level. The most significant changes are seen in the light-quark flavor separation, and in increased precision in the a e-mail: stefano.forte@mi.infn.it determination of the gluon. We explore the implications of NNPDF3.1 for LHC phenomenology at Run II, compare with recent LHC measurements at 13 TeV, provide updated predictions for Higgs production cross-sections and discuss the strangeness and charm content of the proton in light of our improved dataset and methodology. The NNPDF3