Download or read book Spectral Properties of Multi dimensional Quantum Spin Systems written by Amanda M Young and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we analyze spectral properties of frustration-free quantum spin systems, with an emphasis on multi-dimensional models. The focus of this analysis is two-fold. First, we determine the existence or non-existence of a spectral gap above the ground state for a class of multi-dimensional quantum spin systems. Second, we determine a set of criteria for which the spectral gap above the ground state energy of a frustration-free quantum spin system is stable in the presence of local perturbations. We begin by providing the mathematical formulation of quantum spin systems, including a discussion of the thermodynamic limit. We formalize the construction of infinite volume systems when we introduce Lieb-Robinson bounds. When these bounds hold, the dynamics of the finite volume quantum spin systems extend to the thermodynamic limit, and a well-defined infinite volume Hamiltonian, known as the GNS Hamiltonian, is guaranteed to exist. Determining if a quantum spin system is gapped or gapless is a question of the spectrum of the GNS Hamiltonian. It is gapped if there is an interval above the ground state energy that does not contain any points of the spectrum. Otherwise, it is gapless. We show that to prove a gap for the GNS Hamiltonian of a frustration-free system, it suffices to obtain a uniform lower bound for the spectral gap in a sequence of finite volumes. To obtain these results we apply the martingale method, which was first introduced for frustration-free quantum spin systems with open boundary conditions by Nachtergaele in 1996 [48]. We extend this method to hold for periodic boundary conditions, and apply it to the class of pure finitely correlated state models with periodic boundary conditions.We then study the the one-species, multi-dimensional PVBS models and determine the exact collection of model parameters for which the models are gapped in the thermodynamic limit. The PVBS models are a class of particle hopping models where the model parameters dictate the direction a particle prefers to move. We consider these models on two types of infinite volumes. First, we take the thermodynamic limit of the PVBS model to the d-dimensional integer lattice. Second, we consider the PVBS model on a half space of the integer lattice where the boundary is defined by a hyperplane. We find two types of closures of the spectral gap. First, there is a bulk closure due to a critical change in the set of model parameters. The second type of closure is only found in the case of the hyperplane boundary, and is due to the creation of edge states across the boundary. This is inherently different from the bulk closure, as away from the boundary the model still behaves like a gapped system. We then transition to considering the stability of gapped ground state phases. Stability results establish that if a system is gapped, it will remain gapped under the addition of small perturbations. The two main technical tools we use to prove such a result are Lieb-Robinson bounds and the spectral flow. Common to both tools is that they express locality properties for observables under a global evolution. We generalize this notion by introducing the theory of quasi-local maps. We apply our theory to prove the stability result from [47], which holds for both one-dimensional andmulti-dimensional quantum spin systems. The result from [47], which we extend to hold for a larger class of models and boundary conditions, states that a uniformly gapped family of frustration-free Hamiltonians with topologically ordered ground states will remain gapped in the presence of an exponentially decaying perturbation. We conclude with applying the stability result the finitely correlated state models with periodic boundary conditions.

Download or read book Static and Dynamic Properties of low dimensional Quantum Spin Systems written by Simon Nils Grossjohann and published by Cuvillier Verlag. This book was released on 2010-08-17 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In my thesis, static and dynamic properties of low-dimensional spin models were studied by means of a state of the art QMC method (SSE). As one among many numerical algorithms (e.g. DMRG, ED), the QMC proved to be a very flexible and high performance tool with access to dynamic correlation functions at finite temperatures and finite magnetic fields within the thermodynamic limit1. After detailed introduction of the QMC’s basic implementation, I provided yet unpublished information about the measurement of transverse (and longitudinal) imaginary time correlation functions for the spin S Heisenberg model. In addition to that, complications of the analytic continuation to the real axis were explained and two common Maximum Entropy algorithms (Bryan and Meshkov) introduced briefly. In my thesis, both algorithms have been implemented and contrasted in regard to their performance and quality of the continuation, clearly favoring Bryan’s method which is a standard least square algorithm based on Newton iterations with however highly optimized search directions in the multi-dimensional solution space.

Download or read book Tensor Network States and Effective Particles for Low Dimensional Quantum Spin Systems written by Laurens Vanderstraeten and published by Springer. This book was released on 2017-08-10 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.

Download or read book Mathematical Problems in Quantum Physics written by Federico Bonetto and published by American Mathematical Soc.. This book was released on 2018-10-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia. In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models. The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.

Download or read book Properties of Propagation of Quantum Spin Systems written by Derek W. Robinson and published by . This book was released on 197? with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multidimensional Solid State NMR and Polymers written by K. Schmidt-Rohr and published by Academic Press. This book was released on 1994-11-15 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: NMR spectroscopy is the most valuable and versatile analytical tool in chemistry. While excellent monographs exist on high-resolution NMR in liquids and solids, this is the first book to address multidimensional solid-state NMR. Multidimensional techniques enable researchers to obtain detailed information about the structure, dynamics, orientation, and phase separation of solids, which provides the basis of a better understanding of materials properties on the molecular level.Dramatic progress-much of it pioneered by the authors-has been achieved in this area, especially in synthetic polymers. Solid-state NMR now favorably competes with well-established techniques, such as light, x-ray, or neutron scattering, electron microscopy, and dielectric and mechanical relaxation. The application of multidimensional solid-state NMR inevitably involves use of concepts from different fields of science. This book also provides the first comprehensive treatment of both the new experimental techniques and the theoretical concepts needed in more complex data analysis. The text addresses spectroscopists and polymer scientists by treating the subject on different levels; descriptive, technical, and mathematical approaches are used when appropriate. It presents an overview of new developments with numerous experimental examples and illustrations, which will appeal to readers interested in both the information content as well as the potential of solid-state NMR. The book also contains many previously unpublished details that will be appreciated by those who want to perform the experiments. The techniques described are applicable not only to the study of synthetic polymers but to numerous problems in solid-state physics, chemistry, materials science, and biophysics. Presents original theories and new perspectives on scattering techniques Provides a systematic treatment of the whole subject Gives readers access to previously unpublished material Includes extensive illustrations

Download or read book Perturbative Continuous Unitary Transformations Spectral Properties of Low Dimensional Spin Systems written by Christian Knetter and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Theory and Mathematical Physics A Festschrift in Honor of Barry Simon s 60th Birthday written by Fritz Gesztesy and published by American Mathematical Soc.. This book was released on 2007 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.

Download or read book Quantum Classical Correspondence written by Bei-Lok Hu and published by International Press of Boston. This book was released on 1997 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1988, a series of conferences held at Drexel University provided a forum on quantum chaos and related topics. The fourth conference, the proceedings of which are recorded here, broadens that theme to the unifying question of quantum classical correspondence.

Download or read book Frustrated Spin Systems written by H. T. Diep and published by World Scientific. This book was released on 2013 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers all principal aspects of currently investigated frustrated systems, from exactly solved frustrated models to real experimental frustrated systems, going through renormalization group treatment, Monte Carlo investigation of frustrated classical Ising and vector spin models, low-dimensional systems, spin ice and quantum spin glass. The reader can OCo within a single book OCo obtain a global view of the current research development in the field of frustrated systems.This new edition is updated with recent theoretical, numerical and experimental developments in the field of frustrated spin systems. The first edition of the book appeared in 2005. In this edition, more recent works until 2012 are reviewed. It contains nine chapters written by researchers who have actively contributed to the field. Many results are from recent works of the authors.The book is intended for postgraduate students as well as researchers in statistical physics, magnetism, materials science and various domains where real systems can be described with the spin language. Explicit demonstrations of formulas and full arguments leading to important results are given where it is possible to do so."

Download or read book Transport Properties of Low dimensional Quantum Spin Systems written by Fabian Heidrich-Meisner and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partitioning a Many Dimensional Containment Space written by Dr. Martin Concoyle and published by Trafford Publishing. This book was released on 2014-01-14 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the simple math patterns used to describe fundamental, stable, spectral-orbital physical systems (represented as discrete hyperbolic shapes). The containment set has many dimensions, and these dimensions possess macroscopic geometric properties (which are discrete hyperbolic shapes). Thus, it is a description that transcends the idea of materialism (i.e., it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy and which has a natural structure for memory, where this construct is made in relation to the main property of the description being the spectral properties of both material systems and of the metric-spaces that contain the material systems, where material is simply a lower dimension metric-space and where both material components and metric-spaces are in resonance with the containing space.

Download or read book Nuclear Magnetic Resonance written by G A Webb and published by Royal Society of Chemistry. This book was released on 2007-10-31 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a spectroscopic method, Nuclear Magnetic Resonance (NMR) has seen spectacular growth over the past two decades, both as a technique and in its applications. Today the applications of NMR span a wide range of scientific disciplines, from physics to biology to medicine. Each volume of Nuclear Magnetic Resonance comprises a combination of annual and biennial reports which together provide comprehensive of the literature on this topic. This Specialist Periodical Report reflects the growing volume of published work involving NMR techniques and applications, in particular NMR of natural macromolecules which is covered in two reports: "NMR of Proteins and Acids" and "NMR of Carbohydrates, Lipids and Membranes". For those wanting to become rapidly acquainted with specific areas of NMR, this title provides unrivalled scope of coverage. Seasoned practitioners of NMR will find this an in valuable source of current methods and applications. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis.

Download or read book Fundamentals of Solid State Engineering written by Manijeh Razeghi and published by Springer. This book was released on 2018-08-21 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a multidisciplinary introduction to quantum mechanics, solid state physics, advanced devices, and fabrication Covers wide range of topics in the same style and in the same notation Most up to date developments in semiconductor physics and nano-engineering Mathematical derivations are carried through in detail with emphasis on clarity Timely application areas such as biophotonics , bioelectronics

Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 1162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optical Properties Of Solids Proceedings Of The Taiwan japan Workshop On Solid state Optical Spectroscopy written by Hui Pak Ming and published by #N/A. This book was released on 1991-10-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains review articles on solid-state spectroscopies by leading researchers in Japan and Taiwan. Topics include excitons and biexcitons, size effects in quantum dots and microcrystals, nonlinear optical properties, optical spectra of disordered systems, electronic and optical properties of metal-dielectric and semiconductor superlattices, photoemission, Raman spectroscopy, and photoreflectance studies on solids.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: