A short proof of stability of topological order under local perturbations

Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed Hamiltonian $H_0$ can be written as a sum of local pairwise commuting projectors on a $D$-dimensional lattice. We consider a perturbed Hamiltonian $H=H_0+V$ involving a generic perturbation $V$ that can be written as a sum of short-range bounded-norm interactions. We prove that if the strength of $V$ is below a constant threshold value then $H$ has well-defined spectral bands originating from the low-lying eigenvalues of $H_0$. These bands are separated from the rest of the spectrum and from each other by a constant gap. The width of the band originating from the smallest eigenvalue of $H_0$ decays faster than any power of the lattice size.Comment: 15 page

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an $s$-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the {\em spectral flow}, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models $H(s), 0\leq s\leq 1$.Comment: Updated acknowledgments and new email address of S

Derivative moments for characteristic polynomials from the CUE

We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standing conjecture from random matrix theory.Comment: 31 pages, 3 figure

Prevalence of Frailty in European Emergency Departments (FEED): an international flash mob study

Introduction Current emergency care systems are not optimized to respond to multiple and complex problems associated with frailty. Services may require reconfiguration to effectively deliver comprehensive frailty care, yet its prevalence and variation are poorly understood. This study primarily determined the prevalence of frailty among older people attending emergency care. Methods This cross-sectional study used a flash mob approach to collect observational European emergency care data over a 24-h period (04 July 2023). Sites were identified through the European Task Force for Geriatric Emergency Medicine collaboration and social media. Data were collected for all individuals aged 65 + who attended emergency care, and for all adults aged 18 + at a subset of sites. Variables included demographics, Clinical Frailty Scale (CFS), vital signs, and disposition. European and national frailty prevalence was determined with proportions with each CFS level and with dichotomized CFS 5 + (mild or more severe frailty). Results Sixty-two sites in fourteen European countries recruited five thousand seven hundred eighty-five individuals. 40% of 3479 older people had at least mild frailty, with countries ranging from 26 to 51%. They had median age 77 (IQR, 13) years and 53% were female. Across 22 sites observing all adult attenders, older people living with frailty comprised 14%. Conclusion 40% of older people using European emergency care had CFS 5 + . Frailty prevalence varied widely among European care systems. These differences likely reflected entrance selection and provide windows of opportunity for system configuration and workforce planning

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease