Reconstructing the spatial structure of quantum correlations

Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at arbitrary mutual distance. Using neutron scattering data on the compound KCuF$_3$ \unicode{x2014} a system of weakly coupled $S=1/2$ Heisenberg chains \unicode{x2014} and of numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a new emergent length of quantum-mechanical origin \unicode{x2014} the quantum coherence length \unicode{x2014} which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials.Comment: Main text: 8 pages, 5 figures. Supplementary information: 4 pages, 5 figure

Integration of machine learning with neutron scattering for the Hamiltonian tuning of spin ice under pressure

Quantum materials research requires co-design of theory with experiments and involves demanding simulations and the analysis of vast quantities of data, usually including pattern recognition and clustering. Artificial intelligence is a natural route to optimise these processes and bring theory and experiments together. Here, we propose a scheme that integrates machine learning with high-performance simulations and scattering measurements, covering the pipeline of typical neutron experiments. Our approach uses nonlinear autoencoders trained on realistic simulations along with a fast surrogate for the calculation of scattering in the form of a generative model. We demonstrate this approach in a highly frustrated magnet, Dy2Ti2O7, using machine learning predictions to guide the neutron scattering experiment under hydrostatic pressure, extract material parameters and construct a phase diagram. Our scheme provides a comprehensive set of capabilities that allows direct integration of theory along with automated data processing and provides on a rapid timescale direct insight into a challenging condensed matter system.Fil: Samarakoon, Anjana. Oak Ridge National Laboratory; Estados Unidos. Argonne National Laboratory; Estados UnidosFil: Tennant, D. Alan. Oak Ridge National Laboratory; Estados UnidosFil: Ye, Feng. Oak Ridge National Laboratory; Estados UnidosFil: Zhang, Qiang. Oak Ridge National Laboratory; Estados UnidosFil: Grigera, Santiago Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin

Internal construct validity of the Warwick-Edinburgh Mental Well-being Scale (WEMWBS): a Rasch analysis using data from the Scottish Health Education Population Survey

Background: The Warwick-Edinburgh Mental Well-Being Scale (WEMWBS) was developed to meet demand for instruments to measure mental well-being. It comprises 14 positively phrased Likert-style items and fulfils classic criteria for scale development. We report here the internal construct validity of WEMWBS from the perspective of the Rasch measurement model. Methods: The model was applied to data collected from 779 respondents in Wave 12 (Autumn 2006) of the Scottish Health Education Population Survey. Respondents were aged 16–74 (average 41.9) yrs. Results: Initial fit to model expectations was poor. The items 'I've been feeling good about myself', 'I've been interested in new things' and 'I've been feeling cheerful' all showed significant misfit to model expectations, and were deleted. This led to a marginal improvement in fit to the model. After further analysis, more items were deleted and a strict unidimensional seven item scale (the Short Warwick Edinburgh Mental Well-Being Scale (SWEMWBS)) was resolved. Many items deleted because of misfit with model expectations showed considerable bias for gender. Two retained items also demonstrated bias for gender but, at the scale level, cancelled out. One further retained item 'I've been feeling optimistic about the future' showed bias for age. The correlation between the 14 item and 7 item versions was 0.954. Given fit to the Rasch model, and strict unidimensionality, SWEMWBS provides an interval scale estimate of mental well-being. Conclusion: A short 7 item version of WEMWBS was found to satisfy the strict unidimensionality expectations of the Rasch model, and be largely free of bias. This scale, SWEMWBS, provides a raw score-interval scale transformation for use in parametric procedures. In terms of face validity, SWEMWBS presents a more restricted view of mental well-being than the 14 item WEMWBS, with most items representing aspects of psychological and eudemonic well-being, and few covering hedonic well-being or affect. However, robust measurement properties combined with brevity make SWEMWBS preferable to WEMWBS at present for monitoring mental well-being in populations. Where face validity is an issue there remain arguments for continuing to collect data on the full 14 item WEMWBS

Multipartite entanglement in the 1-D spin-12\frac{1}{2} Heisenberg Antiferromagnet

Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the Quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as $T\rightarrow 0$. We argue that this implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale that is determined by universal properties, up to a non-universal amplitude. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. The 1D spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges non-trivially as $\sim \log(1/T)^{3/2}$. We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF$_3$, a material well-described by the Heisenberg chain.Comment: 8 pages and 3 figures; 1 page and 1 figure of the appendix; typos corrected; references adde

Hidden local symmetry breaking in a kagome-lattice magnetic Weyl semimetal

Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co$_{3}$Sn$_{2}$S$_{2}$, a new discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below $T_{C}$ in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symmetry breaking surprisingly co-emerges with the onset of ferromagnetic order in Co$_{3}$Sn$_{2}$S$_{2}$, by a combined use of neutron total scattering and half polarized neutron diffraction. The mismatch of local and average symmetries occurs below $T_{C}$, indicating that Co$_{3}$Sn$_{2}$S$_{2}$ evolves to an intrinsically lattice disordered system when the ferromagnetic order is established. The local symmetry breaking with intrinsic lattice disorder provides new understandings to the puzzling magnetic properties. Our density function theory calculation indicates that the local symmetry breaking is expected to reorient local ferromagnetic moments, unveiling the existence of the ferromagnetic instability associated with the lattice instability. Furthermore, DFT calculation unveils that the local symmetry breaking could affect the Weyl property by breaking mirror plane. Our findings highlight the fundamentally important role that the local symmetry breaking plays in advancing our understanding on the magnetic and topological properties in Co$_{3}$Sn$_{2}$S$_{2}$, which may draw the attention to explore the overlooked local symmetry breaking in Co$_{3}$Sn$_{2}$S$_{2}$, its derivatives, and more broadly in other topological Dirac/Weyl semimetals and kagome-lattice magnets.Comment: 35 pages, 6 figures, 1 table, 1 Supplementary Informatio

Quantifying and controlling entanglement in the quantum magnet Cs2_2CoCl4_4

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs$_2$CoCl$_4$, a close realization of the $S=1/2$ transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one- and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.Comment: Main text: 7 pages, 4 figures. Supplementary Information: 15 pages, 15 figure

Rasch analysis of the hospital anxiety and depression scale (hads) for use in motor neurone disease

<p>Abstract</p> <p>Background</p> <p>The Hospital Anxiety and Depression Scale (HADS) is commonly used to assess symptoms of anxiety and depression in motor neurone disease (MND). The measure has never been specifically validated for use within this population, despite questions raised about the scale's validity. This study seeks to analyse the construct validity of the HADS in MND by fitting its data to the Rasch model.</p> <p>Methods</p> <p>The scale was administered to 298 patients with MND. Scale assessment included model fit, differential item functioning (DIF), unidimensionality, local dependency and category threshold analysis.</p> <p>Results</p> <p>Rasch analyses were carried out on the HADS total score as well as depression and anxiety subscales (HADS-T, D and A respectively). After removing one item from both of the seven item scales, it was possible to produce modified HADS-A and HADS-D scales which fit the Rasch model. An 11-item higher-order HADS-T total scale was found to fit the Rasch model following the removal of one further item.</p> <p>Conclusion</p> <p>Our results suggest that a modified HADS-A and HADS-D are unidimensional, free of DIF and have good fit to the Rasch model in this population. As such they are suitable for use in MND clinics or research. The use of the modified HADS-T as a higher-order measure of psychological distress was supported by our data. Revised cut-off points are given for the modified HADS-A and HADS-D subscales.</p