Quantum critical scaling of the geometric tensors

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.Comment: Typos correcte

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

On the optimal feedback control of linear quantum systems in the presence of thermal noise

We study the possibility of taking bosonic systems subject to quadratic Hamiltonians and a noisy thermal environment to non-classical stationary states by feedback loops based on weak measurements and conditioned linear driving. We derive general analytical upper bounds for the single mode squeezing and multimode entanglement at steady state, depending only on the Hamiltonian parameters and on the number of thermal excitations of the bath. Our findings show that, rather surprisingly, larger number of thermal excitations in the bath allow for larger steady-state squeezing and entanglement if the efficiency of the optimal continuous measurements conditioning the feedback loop is high enough. We also consider the performance of feedback strategies based on homodyne detection and show that, at variance with the optimal measurements, it degrades with increasing temperature.Comment: 10 pages, 2 figures. v2: minor changes to the letter; better explanation of the necessary and sufficient conditions to achieve the bounds (in the supplemental material); v3: title changed; comparison between optimal general-dyne strategy and homodyne strategy is discussed; supplemental material included in the manuscript and few references added. v4: published versio

Ground state fidelity and quantum phase transitions in free Fermi systems

We compute the fidelity between the ground states of general quadratic fermionic hamiltonians and analyze its connections with quantum phase transitions. Each of these systems is characterized by a $L\times L$ real matrix whose polar decomposition, into a non-negative $\Lambda$ and a unitary $T$, contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of $\Lambda$. This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exemplification by a model of fermions on a totally connected graph.Comment: 4 pages, 2 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.

Biomarker-guided trials: Challenges in practice.

Biomarker-guided trials have drawn considerable attention as they promise to lead to improvements in the benefit-risk ratio of treatments and enhanced opportunities for drug development. A variety of such designs have been proposed in the literature, many of which have been adopted in practice. Implementing such trial designs in practice can be challenging, and identifying those challenges was the main objective of a workshop organised by the MRC Hubs for Trials Methodology Research Network's Stratified Medicine Working Group in March 2017. Participants reflected on completed and ongoing biomarker-guided trials to identify the practical challenges encountered. Here, the key challenges identified during the workshop including those related to funding, ethical and regulatory issues, recruitment, monitoring of samples and laboratories, biomarker assessment, and data sharing and resources, are discussed. Despite the complexities often associated with biomarker-guided trials, the workshop concluded that they can play an important role in advancing the field of personalised medicine. Therefore, it is important that the practical challenges surrounding their implementation are acknowledged and addressed

Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behavior of the theory at first order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic

Social Transmission and the Spread of Modern Contraception in Rural Ethiopia

Socio-economic development has proven to be insufficient to explain the time and pace of the human demographic transition. Shifts to low fertility norms have thus been thought to result from social diffusion, yet to date, micro-level studies are limited and are often unable to disentangle the effect of social transmission from that of extrinsic factors. We used data which included the first ever use of modern contraception among a population of over 900 women in four villages in rural Ethiopia, where contraceptive prevalence is still low (<20%). We investigated whether the time of adoption of modern contraception is predicted by (i) the proportion of ever-users/non ever-users within both women and their husbands' friendships networks and (ii) the geographic distance to contraceptive ever-users. Using a model comparison approach, we found that individual socio-demographic characteristics (e.g. parity, education) and a religious norm are the most likely explanatory factors of temporal and spatial patterns of contraceptive uptake, while the role of person-to-person contact through either friendship or spatial networks remains marginal. Our study has broad implications for understanding the processes that initiate transitions to low fertility and the uptake of birth control technologies in the developing world