Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes

We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the 1D Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance $r$ as $1/r^\alpha$, as well as a related class of fermionic Hamiltonians that generalise the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents $\alpha$, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for $\alpha \lesssim1$, while connected correlation functions can decay with a hybrid exponential and power-law behaviour, with a power that is $\alpha$-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every $\alpha$. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough $\alpha$. For the fermionic models we show that the edge modes, massless for $\alpha \gtrsim 1$, can acquire a mass for $\alpha < 1$. The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.Comment: 15 pages, 8 figure

How Providing Care For Individuals With Dementia Affects How A Caregiver Changes Their Lifestyle: A Focus on the Positives

Background/significance Caregivers of individuals with dementia (e.g. Alzheimer’s Disease) may change their day-to-day life, especially self-care, to meet the needs of the person with dementia, which can be detrimental to their health. Caregivers for individuals with dementia experience both primarily negative and primarily positive effects on physical and mental health through exposure to the effects of dementia. Caregivers often report substandard self-care practices and unpleasant impacts on mental health. Others report notable beneficial influences within different aspects of their life. The positive effects have not been widely researched in literature. Purpose The objective of this research study is to understand how caregivers of individuals with dementia change their day-to-day life due to the impact of caregiving in aspects including physical and mental health, in an effort to determine ways to enhance caregiver\u27s coping methods and promote positive outcomes for both personal and professional caregivers. Methods The general population included in this study are caregivers of individuals with dementia. To be included in the study, one must be (or previously have been) either a personal or professional caregiver of an individual with dementia, of any sex, over 18 years of age. Those who were excluded from this study included caregivers of non-dementia patients and caregivers under the age of 18. To understand the impact of caring for an individual with dementia, a qualitative research study was conducted to answer the research question “How does providing care for an individual with dementia affect how a caregiver changes their lifestyle?” The study was implemented as 2 follows: a sample of 16 caregivers participated in a qualitative interview process to provide insight into their personal opinions on how caregiving for an individual with dementia (personally, professionally, or voluntarily) affects or has affected their well-being. An interview process developed for the study was followed, which included demographic data and questions about the caregiver’s life and activities. Each interview lasted an average of between 15 and 30 minutes. The interviews were transcribed and cross-analyzed to search for the common themes of physical activity, eating habits and diet, spirituality, mental health, lifestyle, and outlook on life. Advice to enhance a positive experience for future caregivers, as well as additional resources that the participants think are necessary to improve the positive effects of caregiver, were also analyzed. Results Although there was a prevalently negative impact on caregivers’ eating habits and mental health, each other category proved to be either neutral or positive. The category with the most positive outcome was outlook on life. Qualitative interviews disclosed the excessive levels of stress experienced by every caregiver of an individual with dementia, but in turn, each participant communicated the strategies they found to be effective to cope with the negative effects of caring for someone with dementia. Conclusion Implications Those who care for individuals with dementia, whether on a personal or professional basis, must make sure to take care of their personal physical and mental health as well as that of their patients, to avoid the detrimental effects that caregiving for an individual with dementia ultimately have on a caregiver. The results of this research study can be used for a greater understanding of the impact of caregiving for individuals with dementia. Current and future caregivers can use the results of this study to recognize which aspects of their life that they 3 may need to focus more on while caregiving in order to stay healthy, and take the advice offered by the participants to promote an overall positive experience. Further research on how to improve the number of positive outcomes in each aspect of self-care for caregivers can be conducted based on the results of this study

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale $\tau$ . The time evolution of the entanglement entropy displays different regimes depending on the value of $\tau$, showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of entanglement entropy and Schmidt gap.Comment: Accepted for publication in Phys. Rev.

Kitaev chains with long-range pairing

We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions.Comment: 5+3 pages, 4+2 figure

Magnetic properties of commensurate Bose-Bose mixtures in one-dimensional optical lattices

We investigate magnetic properties of strongly interacting bosonic mixtures confined in one dimensional geometries, focusing on recently realized Rb-K gases with tunable interspecies interactions. By combining analytical perturbation theory results with density-matrix-renormalization group calculations, we provide quantitative estimates of the ground state phase diagram as a function of the relevant microscopic quantities, identifying the more favorable experimental regimes in order to access the various magnetic phases. Finally, we qualitatively discuss the observability of such phases in realistic setups when finite temperature effects have to be considered.Comment: 9 pages, 7 figures, to be published in EPJ ST special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases

Loops and Strings in a Superconducting Lattice Gauge Simulator

We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1 representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.Comment: 17 pages, 5 figures. Published versio

Energy saving in typical architecture: The flow energy in traditional solutions in a sustainable perspective

Quick urbanization increment causes a few difficult problems, such as social assessment, more energy demands, and pollution increase. A positive factor for a city is the concentration of energy requests. On the other hand, urbanization trend is going to fragmentation of settlements, with a consequent expansion of the energy distribution networks but also an increase of the energy wasted. Each building needs some of the total energy distributed in the city. Energy needs can be grouped into four essential parameters: construction, heating, electricity, and water. How were these four parameters satisfied in the XIX century, before the industrial revolution? In those days' energy requirement wasn't so high and could be supplied with basic energy production technology. The knowledge of appropriate building technology (project), the use of (energy saving) materials, with a low and punctual heating system (fireplace, stove) or passive refreshment all intervened in this process. These requirements were achieved in each country using building plans studied to face different weather conditions with different architectural typology and with human effort and time (work-energy). This paper analyses an energy balance in a single typical building in the center of Italy, describing the energy flow that will show the logical and technical solution for "energy-saving". Old buildings (before the introduction of "building-plant") were always designed and built with an energy-saving concern. This article wants to propose the study of a typical building in which are used only low-energy systems to meet all the comfort requirements, to demonstrate that it is not necessary to use high-energy technology. This is how architecture urbanization studies and implementation can be used to reduce high-energy production needs. © 2019 Author(s)

Fundamental thresholds of realistic quantum error correction circuits from classical spin models

Mapping the decoding of quantum error correcting (QEC) codes to classical disordered statistical mechanics models allows one to determine critical error thresholds of QEC codes under phenomenological noise models. Here, we extend this mapping to admit realistic, multi-parameter noise models of faulty QEC circuits, derive the associated strongly correlated classical spin models, and illustrate this approach for a quantum repetition code with faulty stabilizer readout circuits. We use Monte-Carlo simulations to study the resulting phase diagram and benchmark our results against a minimum-weight perfect matching decoder. The presented method provides an avenue to assess fundamental thresholds of QEC circuits, independent of specific decoding strategies, and can thereby help guiding the development of near-term QEC hardware

Building performance monitoring: From in-situ measurement to regression-based approaches

Simple and robust data analysis methodologies are crucial to learn insights from measured data and reduce the performance gap in building stock. For this reason, continuous performance monitoring should become a more diffuse practice in order to improve our design and operation strategies for the future. The research presented aims to highlight potential links between experimental approaches for test-facilities and methods and tools used for continuous performance monitoring, at the state of the art. In particular, we explore the relation between ISO 9869:2014 method for in-situ measurement of thermal transmittance (U) and regression-based monitoring approaches, such as co-heating test and energy signature, for heat load coefficient (HLC) and solar aperture (gA) estimation. In particular, we highlight the robustness and scalability of these monitoring techniques, considering relevant issues in current integrated engineer design perspective. These issues include, among others, the necessity of limiting the number of a sensors to be installed in buildings, the possibility of employing both experimental and real operation data and, finally, the possibility to automate and perform monitoring at multiple scales, from single components, to individual buildings, to building stock and cities