Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice

We study an SU(2) symmetric spin-3/2 model on the z=3 Bethe lattice using the infinite Time Evolving Block Decimation (iTEBD) method. This model is shown to exhibit a rich phase diagram. We compute the expectation values of several order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, a anti-ferromagnetic as well as a dimerized phase. We calculate the entanglement spectra from which we conclude the existence of a symmetry protected topological phase that is characterized by S=1/2 edge spins. Details of the iTEBD algorithm used for the simulations are included

Recovery from Work-Related Stress: A literature review

Occupational stress adversely affects both the individual and the organization. Because of its economical and health relevance, much research has been devoted to employee recovery from work stress. Defined as a process of replenishing resources, recovery has been suggested to be important in reducing work-related fatigue, thereby making individuals feeling ready again to meet the demands at work. This literature review systematically summarizes findings from research on recovery. The literature search was conducted based on the PsychInfo database. Forty-eight journal articles were included in the review. Overall, studies consistently implicate that daily recovery is especially important to avoid long-term strain reactions. Moreover, research has found specific off-job activities as well as experiences attached to these activities to promote recovery, thereby improving performance, health, and well-being. Taken together, results imply that both individuals and organizations should be concerned about employee recovery and possibilities to support it during work and non-work time

Nature of the spin-liquid ground state of the S=1/2 Heisenberg model on the kagome lattice

We perform a density-matrix renormalization group (DMRG) study of the S = 1/2 Heisenberg anti-ferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16 000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions, and finite topological entanglement gamma consistent with gamma = log(2)2, ruling out gapless, chiral, or nontopological spin liquids in favor of a topological spin liquid of quantum dimension 2, with strong evidence for a gapped topological Z(2) spin liquid

Tensor networks for the simulation of strongly correlated systems

This thesis treats the classical simulation of strongly-interacting many-body quantum-mechanical systems in more than one dimension using matrix product states and the more general tensor product states. Contrary to classical systems, quantum many-body systems possess an exponentially larger number of degrees of freedom, thereby significantly complicating their numerical treatment on a classical computer. For this thesis two different representations of quantum many-body states were employed. The first, the so-called matrix product states (MPS) form the basis for the extremely successful density matrix renormalization group (DMRG) algorithm. While originally conceived for one-dimensional systems, MPS are in principle capable of describing arbitrary quantum many-body states. Using concepts from quantum information theory it is possible to show that MPS provide a representation of one-dimensional quantum systems that scales polynomially in the number of particles, therefore allowing an efficient simulation of one-dimensional systems on a classical computer. One of the key results of this thesis is that MPS representations are indeed efficient enough to describe even large systems in two dimensions, thereby enabling the simulation of such systems using DMRG. As a demonstration of the power of the DMRG algorithm, it is applied to the Heisenberg antiferromagnet with spin $S = 1/2$ on the kagome lattice. This model's ground state has long been under debate, with proposals ranging from static spin configurations to so-called quantum spin liquids, states where quantum fluctuations destroy conventional order and give rise to exotic quantum orders. Using a fully $SU(2)$-symmetric implementation allowed us to handle the exponential growth of entanglement and to perform a large-scale study of this system, finding the ground state for cylinders of up to 700 sites. Despite employing a one-dimensional algorithm for a two-dimensional system, we were able to compute the spin gap (i.e. the energy gap to the first spinful excitation) and study the ground state properties, such as the decay of correlation functions, the static spin structure factors, and the structure and distribution of the nearest-neighbor spin-spin correlations. Additionally, by applying a new tool from quantum information theory, the topological entanglement entropy, we could also with high confidence demonstrate the ground state of this model to be the elusive gapped $Z_2$ quantum spin liquid with topological order. To complement this study, we also considered the extension of MPS to higher dimensions, known as tensor product states (TPS). We implemented an optimization algorithm exploiting symmetries for this class of states and applied it to the bilinear-biquadratic-bicubic Heisenberg model with spin $S=3/2$ on the $z=3$ Bethe lattice. By carefully analyzing the simulation data we were able to determine the presence of both conventional and symmetry-protected topological order in this model, thereby demonstrating the analytically predicted existence of the Haldane phase in higher dimensions within an extended region of the phase diagram. Key properties of this symmetry-protected topological order include a doubling of the levels in the entanglement spectrum and the presence of edge spins, both of which were confirmed in our simulations. This finding simultaneously validated the applicability of the novel TPS algorithms to the search for exotic order

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

In magnetically ordered systems, the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite-size energy spectra, the so-called tower of states (TOS). In the present work, we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground-state entanglement spectrum (ES). Using state-of-the-art density matrix renormalization group (DMRG) calculations, we examine the ES of the 2D antiferromagnetic J(1)-J(2) Heisenberg model on both the triangular and kagome lattice. At large ferromagnetic J(2), the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite-size scaling in the thermodynamic limit) sharply reflects TOS features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes, TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG

Project Assessment Framework through Design (PAFTD) - A Project Assessment Framework in Support of Strategic Decision Making

Research and development organizations that push the innovation edge of technology frequently encounter challenges when attempting to identify an investment strategy and to accurately forecast the cost and schedule performance of selected projects. Fast moving and complex environments require managers to quickly analyze and diagnose the value of returns on investment versus allocated resources. Our Project Assessment Framework through Design (PAFTD) tool facilitates decision making for NASA senior leadership to enable more strategic and consistent technology development investment analysis, beginning at implementation and continuing through the project life cycle. The framework takes an integrated approach by leveraging design principles of useability, feasibility, and viability and aligns them with methods employed by NASA's Independent Program Assessment Office for project performance assessment. The need exists to periodically revisit the justification and prioritization of technology development investments as changes occur over project life cycles. The framework informs management rapidly and comprehensively about diagnosed internal and external root causes of project performance

Phase diagram of the J1-J2 Heisenberg model on the kagome lattice

We perform an extensive density matrix renormalization group (DMRG) study of the ground-state phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J_2=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J_2\approx 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J_2 the ground state displays signatures of the magnetic order of the \sqrt{3}\times\sqrt{3} and the q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.Comment: 9 pages, 10 figures. Figure added, minor modifications, as publishe

Crop Harvesting

Das Jahr 2020 war in vielen Bereich der Landwirtschaft wieder ein schwieriges Jahr. Vor allem die Situation für Vieh- und Milchbetriebe ist aufgrund niedriger Erzeugerpreise angespannt. Es zeigen sich die ersten Auswirkungen auf den Maschinenabsatz in der Sparte Halmgutbergung. Ein deutlicher Rückgang zeigt sich bei den selbstfahrenden Feldhäckslern. Hier wurden auch nur wenige neue Entwicklungen vorgestellt. Der Hersteller Krone zeigt mit einem Funktionsmuster für einen leistungsstarken Anbauhäcksler eine Alternative zu den Selbstfahrern. Der Absatz der Ballenpressen konnte nicht an die guten Verkaufszahlen der Vorjahre anknüpfen. Es zeigen sich jedoch Trends hin zu höherem Bedienkomfort und bei den Press-Wickel-Kombinationen zur Folienbindung. Im Bereich der Ladewagen wird die Situation weniger kritisch eingeschätzt. Hier wird auf verbesserte Fahrwerke gesetzt, um den Boden noch besser zu schonen. Mit Iveco steigt ein neuer Hersteller in den Bereich der Agro-Trucks ein.2020 was another difficult year in many agricultural sectors. The situation for livestock and dairy farms was particularly tense due to low producer prices. First impacts appear as reduced sales figures in the segment of forage harvesting technology. A clear decline can be seen for self-propelled forage harvesters, and only a few new developments were presented here. The manufacturer Krone showed a functional demonstrator of a new tractor-mounted high-output forage harvester as an alternative to the selfpropelled machines. The sale figures of balers couldn't match the good numbers of previous years. However, there is a trend towards greater ease of use and, in the case of baler with bale wrappers, towards film binding. In the segment of loading wagons the situation is less tense. The last developments focused on even better soil protection with improved undercarriages. Iveco, a new manufacturer, enters the agro-truck sector