Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.Comment: Revised version, typos corrected, references added, 31 page

Mediating effect of pubertal stages on the family environment and neurodevelopment: An open-data replication and multiverse analysis of an ABCD Study®

Contains fulltext : 285495.pdf (Publisher’s version ) (Open Access)Increasing evidence demonstrates that environmental factors meaningfully impact the development of the brain (Hyde et al., 2020; McEwen and Akil, 2020). Recent work from the Adolescent Brain Cognitive Development (ABCD) Study® suggests that puberty may indirectly account for some association between the family environment and brain structure and function (Thijssen et al., 2020). However, a limited number of large studies have evaluated what, how, and why environmental factors impact neurodevelopment. When these topics are investigated, there is typically inconsistent operationalization of variables between studies which may be measuring different aspects of the environment and thus different associations in the analytic models. Multiverse analyses (Steegen et al., 2016) are an efficacious technique for investigating the effect of different operationalizations of the same construct on underlying interpretations. While one of the assets of Thijssen et al. (2020) was its large sample from the ABCD data, the authors used an early release that contained 38% of the full ABCD sample. Then, the analyses used several 'researcher degrees of freedom' (Gelman and Loken, 2014) to operationalize key independent, mediating and dependent variables, including but not limited to, the use of a latent factor of preadolescents' environment comprised of different subfactors, such as parental monitoring and child-reported family conflict. While latent factors can improve reliability of constructs, the nuances of each subfactor and measure that comprise the environment may be lost, making the latent factors difficult to interpret in the context of individual differences. This study extends the work of Thijssen et al. (2020) by evaluating the extent to which the analytic choices in their study affected their conclusions. In Aim 1, using the same variables and models, we replicate findings from the original study using the full sample in Release 3.0. Then, in Aim 2, using a multiverse analysis we extend findings by considering nine alternative operationalizations of family environment, three of puberty, and five of brain measures (total of 135 models) to evaluate the impact on conclusions from Aim 1. In these results, 90% of the directions of effects and 60% of the p-values (e.g. p > .05 and p < .05) across effects were comparable between the two studies. However, raters agreed that only 60% of the effects had replicated. Across the multiverse analyses, there was a degree of variability in beta estimates across the environmental variables, and lack of consensus between parent reported and child reported pubertal development for the indirect effects. This study demonstrates the challenge in defining which effects replicate, the nuance across environmental variables in the ABCD data, and the lack of consensus across parent and child reported puberty scales in youth.16 p

Block Spin Density Matrix of the Inhomogeneous AKLT Model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.Comment: 20 page

Many body physics from a quantum information perspective

The quantum information approach to many body physics has been very successful in giving new insight and novel numerical methods. In these lecture notes we take a vertical view of the subject, starting from general concepts and at each step delving into applications or consequences of a particular topic. We first review some general quantum information concepts like entanglement and entanglement measures, which leads us to entanglement area laws. We then continue with one of the most famous examples of area-law abiding states: matrix product states, and tensor product states in general. Of these, we choose one example (classical superposition states) to introduce recent developments on a novel quantum many body approach: quantum kinetic Ising models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of correlated electron systems". Improved version new references adde

Socioeconomic disparities in physical health among Aboriginal and Torres Strait Islander children in Western Australia

Objective. Few empirical studies have specifically examined the relationship between socio-economic status (SES) and health in Indigenous populations of Australia. We sought to provide insights into the nature of this relationship by examining socio-economic disparities in physical health outcomes among Aboriginal and Torres Strait Islander children in Western Australia. Design. We used a diverse set of health and SES indicators from a representative survey conducted in 20002002 on the health and development of 5289 Indigenous children aged 017 years in Western Australia. Analysis was conducted using multivariate logistic regression within a multilevel framework. Results. After controlling for age and sex, we found statistically significant socio- economic disparities in health in almost half of the associations that were investigated, although the direction, shape and magnitude of associations differed. For ear infections, recurring chest infections and sensory function problems, the patterns were generally consistent with a positive socio-economic gradient where better health was associated with higher SES. The reverse pattern was found for asthma, accidents and injuries, and oral health problems, although this was primarily observed for area-level SES indicators. Conclusion. Conventional notions of social position and class have some influence on the physical health of Indigenous children, although the diversity of results implies that there are other ways of conceptualising and measuring SES that are important for Indigenous populations. We need to consider factors that relate specifically to Indigenous circumstances and culture in the past and present day, and give more thought to how we measure social position in the Indigenous community, to gain a better understanding of the pathways from SES to Indigenous child health

Closing in on the properties of antihydrogen

Conference review, with some speculation in the closing section

The persistent shadow of the supermassive black hole of M 87: I. Observations, calibration, imaging, and analysis

Galaxie

Macrosocial determinants of population health in the context of globalization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/55738/1/florey_globalization_2007.pd

Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

InstrumentationLarge scale structure and cosmolog

Characterizing and mitigating intraday variability: reconstructing source structure in accreting black holes with mm-VLBI

Instrumentatio