Universal geometric entanglement close to quantum phase transitions

Under successive Renormalization Group transformations applied to a quantum state $\ket{\Psi}$ of finite correlation length $\xi$, there is typically a loss of entanglement after each iteration. How good it is then to replace $\ket{\Psi}$ by a product state at every step of the process? In this paper we give a quantitative answer to this question by providing first analytical and general proofs that, for translationally invariant quantum systems in one spatial dimension, the global geometric entanglement per region of size $L \gg \xi$ diverges with the correlation length as $(c/12) \log{(\xi/\epsilon)}$ close to a quantum critical point with central charge $c$, where $\epsilon$ is a cut-off at short distances. Moreover, the situation at criticality is also discussed and an upper bound on the critical global geometric entanglement is provided in terms of a logarithmic function of $L$.Comment: 4 pages, 3 figure

Large-Mass Ultra-Low Noise Germanium Detectors: Performance and Applications in Neutrino and Astroparticle Physics

A new type of radiation detector, a p-type modified electrode germanium diode, is presented. The prototype displays, for the first time, a combination of features (mass, energy threshold and background expectation) required for a measurement of coherent neutrino-nucleus scattering in a nuclear reactor experiment. The device hybridizes the mass and energy resolution of a conventional HPGe coaxial gamma spectrometer with the low electronic noise and threshold of a small x-ray semiconductor detector, also displaying an intrinsic ability to distinguish multiple from single-site particle interactions. The present performance of the prototype and possible further improvements are discussed, as well as other applications for this new type of device in neutrino and astroparticle physics (double-beta decay, neutrino magnetic moment and WIMP searches).Comment: submitted to Phys. Rev.

Modeling and forecasting daily electricity load curves: a hybrid approach

We propose a hybrid approach for the modeling and the short-term forecasting of electricity loads. Two building blocks of our approach are (1) modeling the overall trend and seasonality by fitting a generalized additive model to the weekly averages of the load and (2) modeling the dependence structure across consecutive daily loads via curve linear regression. For the latter, a new methodology is proposed for linear regression with both curve response and curve regressors. The key idea behind the proposed methodology is dimension reduction based on a singular value decomposition in a Hilbert space, which reduces the curve regression problem to several ordinary (i.e., scalar) linear regression problems. We illustrate the hybrid method using French electricity loads between 1996 and 2009, on which we also compare our method with other available models including the Électricité de France operational model. Supplementary materials for this article are available online