Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories

Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their built-in ability of classifying and studying symmetries, and the efficient numerical calculations they allow. In this work, we introduce a way to extend the set of symmetric PEPS in order to include local gauge invariance and investigate lattice gauge theories with fermionic matter. To this purpose, we provide as a case study and first example, the construction of a fermionic PEPS, based on Gaussian schemes, invariant under both global and local U(1) gauge transformations. The obtained states correspond to a truncated U(1) lattice gauge theory in 2 + 1 dimensions, involving both the gauge field and fermionic matter. For the global symmetry (pure fermionic) case, these PEPS can be studied in terms of spinless fermions subject to a p-wave superconducting pairing. For the local symmetry (fermions and gauge fields) case, we find confined and deconfined phases in the pure gauge limit, and we discuss the screening properties of the phases arising in the presence of dynamical matter

Prediction of hyperaldosteronism subtypes when adrenal vein sampling is unilaterally successful

Objective: Adrenal venous sampling (AVS) is the gold standard to discriminate patients with unilateral primary aldosteronism (UPA) from bilateral disease (BPA). AVS is technically demanding and in cases of unsuccessful cannulation of adrenal veins, the results may not always be interpreted. The aim of our study was to develop diagnostic models to distinguish UPA from BPA, in cases of unilateral successful AVS and the presence of contralateral suppression of aldosterone secretion.Design: Retrospective evaluation of 158 patients referred to a tertiary hypertension unit who underwent AVS. We randomly assigned 110 patients to a training cohort and 48 patients to a validation cohort to develop and test the diagnostic models.Methods: Supervised machine learning algorithms and regression models were used to develop and validate two prediction models and a simple 19-point score system to stratify patients according to their subtype diagnosis.Results: Aldosterone levels at screening and after confirmatory testing, lowest potassium, ipsilateral and contralateral imaging findings at CT scanning, and contralateral ratio at AVS, were associated with a diagnosis of UPA and were included in the diagnostic models. Machine learning algorithms correctly classified the majority of patients both at training and validation (accuracy: 82.9-95.7%). The score system displayed a sensitivity/specificity of 95.2/96.9%, with an AUC of 0.971. A flow-chart integrating our score correctly managed all patients except 3 (98.1% accuracy), avoiding the potential repetition of 77.2% of AVS procedures.Conclusions: Our score could be integrated in clinical practice and guide surgical decision-making in patients with unilateral successful AVS and contralateral suppression

Machine learning applied to ambulatory blood pressure monitoring: a new tool to diagnose autonomic failure?

BACKGROUND: Autonomic failure (AF) complicates Parkinson’s disease (PD) in one-third of cases, resulting in complex blood pressure (BP) abnormalities. While autonomic testing represents the diagnostic gold standard for AF, accessibility to this examination remains limited to a few tertiary referral centers. OBJECTIVE: The present study sought to investigate the accuracy of a machine learning algorithm applied to 24-h ambulatory BP monitoring (ABPM) as a tool to facilitate the diagnosis of AF in patients with PD. METHODS: Consecutive PD patients naïve to vasoactive medications underwent 24 h-ABPM and autonomic testing. The diagnostic accuracy of a Linear Discriminant Analysis (LDA) model exploiting ABPM parameters was compared to autonomic testing (as per a modified version of the Composite Autonomic Symptom Score not including the sudomotor score) in the diagnosis of AF. RESULTS: The study population consisted of n = 80 PD patients (33% female) with a mean age of 64 ± 10 years old and disease duration of 6.2 ± 4 years. The prevalence of AF at the autonomic testing was 36%. The LDA model showed 91.3% accuracy (98.0% specificity, 79.3% sensitivity) in predicting AF, significantly higher than any of the ABPM variables considered individually (hypotensive episodes = 82%; reverse dipping = 79%; awakening hypotension = 74%). CONCLUSION: LDA model based on 24-h ABPM parameters can effectively predict AF, allowing greater accessibility to an accurate and easy to administer test for AF. Potential applications range from systematic AF screening to monitoring and treating blood pressure dysregulation caused by PD and other neurodegenerative disorders

Probing beta decay matrix elements through heavy ion charge exchange reactions

To access information on neutrinoless double beta decay (0νββ) nuclear matrix elements, it has been proposed by the NUMEN collaboration to exploit the analogies between double beta decay processes and double charge exchange (DCE) nuclear reactions, looking in particular at the conditions where the corresponding cross section can be factorized into nuclear reaction and nuclear structure terms. DCE reactions can be treated as a convolution of two correlated or uncorrelated single charge exchange (SCE) processes, resembling 0νββ and 2νββ, respectively. Thus it is important to model first SCE processes, to get a deeper insight into the possibility to factorize the corresponding cross section, so one can gain a better understanding of DCE cross section factorization. In this contribution, DCE reactions are discussed in terms of the convolution of two uncorrelated SCE processes, which should allow one to extract information on 2νββ nuclear matrix elements. These theoretical investigations are performed in close synergy with the experimental activity running at INFN-LNS within the NUMEN project

Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels

We study ultracold atoms subjected to U(2) non-Abelian potentials: we consider gauge potentials having, in the Abelian limit, degenerate Landau levels and we then investigate the effect of general homogeneous non-Abelian terms. The conditions under which the structure of degenerate Landau levels is preserved are classified and discussed. The typical gauge potentials preserving the Landau levels are characterized by a fictitious magnetic field and by an effective spin-orbit interaction, e.g. obtained through the rotation of two-dimensional atomic gases coupled with a tripod scheme. The single-particle energy spectrum can be exactly determined for a class of gauge potentials, whose physical implementation is explicitly discussed. The corresponding Landau levels are deformed by the non-Abelian contribution of the potential and their spin degeneracy is split. The related deformed quantum Hall states for fermions and bosons (in the presence of strong intra-species interaction) are determined far from and at the degeneracy points of the Landau levels. A discussion of the effect of the angular momentum is presented, as well as results for U(3) gauge potentials

Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor