20 research outputs found
Tensor Product Methods and Entanglement Optimization for Ab Initio Quantum Chemistry
No full textThe treatment of high-dimensional problems such as the Schrodinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methodsdeveloped from different perspectives for different purposes in distinct communities already matured to provide a variety of toolscan be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic New wavefunction methods and entanglement optimizations in quantum chemistry at the Workshop on Theoretical Chemistry, February 18-21, 2014, Mariapfarr, Austria. (c) 2015 Wiley Periodicals, Inc
Klassische Simulationen und Quantensimulationen von Vielteilchen-Systemen
No full textThis thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems.
We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems.
Furthermore, we propose new "analog" quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible.Diese Arbeit widmet sich kürzlichen Entwicklungen im Bereich der klassischen Simulationen und der Quantensimulationen von Vielteilchensystemen.
Wir beschreiben neue klassische Algorithmen, die Probleme von konventionellen Methoden wie Renormalisierungsgruppen- oder Monte Carlo Methoden bewältigen. Diese Algorithmen ermöglichen sowohl die Untersuchung von thermischen Eigenschaften zweidimensionaler klassischer Systeme und eindimensionaler Quantensysteme, als auch die Analyse von Grundzuständen und Zeitentwicklungen zweidimensionaler frustrierter oder fermionischer Quantensysteme.
Desweiteren machen wir Vorschläge für "analoge" Quantensimulatoren, die interessante Modelle wie das Tonks-Girardeau Gas oder das frustrierte XY-Modell auf einem trigonalen Gitter realisieren. Diese Simulatoren basieren auf optischen Gittern und Ionenfallen und sind technisch umsetzbar
Evaluation of employee assessment based on selected aspects with special consideration of the information provided on the internet for taxpayers
No full textDiese Arbeit beschäftigt sich mit der Frage, ob alle notwendigen Informationen zur korrekten Durchführung einer Arbeitnehmerveranlagung über Online- als auch literarische Quellen gefunden werden können. Da die Arbeitnehmerveranlagung für Steuerpflichtige jährlich die Möglichkeit bietet, einen Teil der bezahlten Steuern vom Staat zurückerstattet zu bekommen, ist es wichtig, die qualitativ hochwertigsten Quellen ausfindig zu machen. Dazu folgen am Beginn eine kurze Einführung zu den wichtigsten Begriffen im Bereich der Arbeitnehmerveranlagung, sowie eine kurze Vorstellung der untersuchten Quellen. Anhand einer vom Autor erstellten Checkliste, wird ein Vergleich der literarischen- und Onlinequellen ermöglicht. Die Ergebnisse zeigen keinen signifikanten Unterschied zwischen der Qualität von Onlineinformationen oder jenen aus literarischen Werken. Es konnte jedoch gezeigt werden, dass die korrekte Durchführung einer Arbeitnehmerveranlagung auf Grundlage dieser Informationsquellen möglich ist. Zusätzlich erfolgen die Analyse von 100 durchgeführten Arbeitnehmerveranlagungen einer Steuerberatungskanzlei und die Definition der wichtigsten Einflussfaktoren auf eine mögliche Steuergutschrift. Diese Ergebnisse wurden danach mit den Daten der Statistik Austria verglichen. Es konnten deutliche Unterschiede in der durchschnittlichen Höhe der Aufwandsposten (Sonderausgaben, Werbungskosten, außergewöhnliche Belastungen) festgestellt werden. Auch die geringe Korrelation zwischen der Höhe des Einkommens und der möglichen Steuergutschriftshöhe wurde verdeutlicht. Den Abschluss des empirischen Teils stellt ein vom Autor selbsterstelltes, provisionsorientiertes Einkommensmodell für Steuerberater dar, wobei sich die Entlohnung nach der erzielten Steuergutschrift richtet. Abgeschlossen wird die Arbeit von einer kurzen Zusammenfassung, in der nochmals näher auf die verschiedenen Ergebnisse eingegangen wird.This thesis deals with the question whether all necessary information for a correct implementation of an employee tax assessment can be found online and through literary sources. Since the tax assessment for taxpayers annually offers the possibility to get back some of the taxes paid by the state, it is important to find the best sources. At the beginning, a brief introduction to the most important terms is necessary, as well as a brief presentation of the online and literary sources examined. Based on a checklist created by the author, a comparison between online and literary information is possible. The results do not show a significant difference. However, it has been shown that a correct implementation of an employee tax assessment based on both sources is possible. Additionally an analysis of 100 employee tax assessments was made. Using these results the most important influencing factors for a tax credit were defined. Afterwards the results were compared with the Statistics Austria data. Significant differences in the average level of expenditure (special expenses, advertising costs, extraordinary expenses) were identified. Also the low correlation between the amount of income and the possible tax credit was clarified. The conclusion of the empirical part is a self-created, revenue-oriented income model for tax consultants, which is based on the tax credit obtained. The thesis concludes with a brief summary, in which the results are discussed.Mark Michael Murg, Bakk.rer.soc.oec.Abweichender Titel laut Übersetzung des Verfassers/der VerfasserinZusammenfassungen in Deutsch und EnglischMasterarbeit Karl-Franzens-Universität Graz 2017 D1068
Efficient Evaluation of Partition Functions of Inhomogeneous Many-Body Spin Systems
No full textWe present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2D classical spin systems and 1D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite-temperature properties of bosonic particles in 1D optical lattices, as realized in current experiments
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
No full textThis article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states
Exploring frustrated spin systems using projected entangled pair states
No full textWe study the nature of the ground state of the frustrated J(1)-J(2) model and the J(1)-J(3) model using a variational algorithm based on projected entangled pair states. By investigating spin-spin correlation functions, we observe a separation in parameter regions with long- and short-range order. A direct comparison with exact diagonalizations in the subspace of short-range valence bond singlets reveals that the system is well described by states within this subset in the short-range order regions. We discuss the question whether the system forms a spin liquid, a plaquette valence bond crystal, or a columnar dimer crystal in these parameter regions
Simulating strongly correlated quantum systems with tree tensor networks
No full textWe present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density-matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following [Y. Shi, L. Duan, and G. Vidal, Phys. Rev. A 74, 022320 (2006)], we treat a treelike network ansatz with arbitrary coordination number z, where the z=2 case corresponds to the one-dimensional (1D) scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1D interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach
Matrix product operator representations
No full textWe show how to construct relevant families of matrix product operators (MPOs) in one and higher dimensions. These form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translationally invariant MPOs suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We show how these tools can be exploited for constructing new algorithms for simulating quantum spin systems
