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 Static and Dynamic Properties of Low Dimensional Quantum Spin Systems written by Simon Nils Grossjohann and published by . This book was released on 2010 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Algebras and Quantum Statistical Mechanics written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
Download or read book Critical Properties of Quantum Spin Systems at Zero Temperature written by Raimundo Rocha dos Santos and published by . This book was released on 1980 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Entropy and the Quantum II written by Robert Sims and published by American Mathematical Soc.. This book was released on 2011-09-02 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Entropy and the Quantum schools has been to introduce young researchers to some of the exciting current topics in mathematical physics. These topics often involve analytic techniques that can easily be understood with a dose of physical intuition. In March of 2010, four beautiful lectures were delivered on the campus of the University of Arizona. They included Isoperimetric Inequalities for Eigenvalues of the Laplacian by Rafael Benguria, Universality of Wigner Random Matrices by Laszlo Erdos, Kinetic Theory and the Kac Master Equation by Michael Loss, and Localization in Disordered Media by Gunter Stolz. Additionally, there were talks by other senior scientists and a number of interesting presentations by junior participants. The range of the subjects and the enthusiasm of the young speakers are testimony to the great vitality of this field, and the lecture notes in this volume reflect well the diversity of this school.
Download or read book Operator Algebras and Quantum Statistical Mechanics II written by Ola Bratteli and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.
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 Exactly Solved Models and the Physical Properties of Quantum Spin Systems and Quantum Gases written by Norman Oelkers and published by . This book was released on 2006 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Many Degrees of Freedom in Field Theory written by L. Streit and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volumes 30 and 31 of this series, dealing with "Many Degrees of Freedom," contain the proceedings of the 1976 International Summer Institute of Theoretical Physics, held at the university of Bielefeld from August 23 to September 4, 1976. This institute was the eighth in a series of summer schools devoted to particle physics and organized by universities and research institutes in the Federal Republic of Germany. Many degrees of freedom and collective phenomena play a critical role in the description and understanding of elementary particles. The lectures in this volume were intended to display how these structures occur in various recent developments of mathematical physics. Lectures ranged from classical nonlinear field theory over classical soliton models, constructive quantum field theory with soliton solutions and gauge models to the recent unified description of renormalization group tech niques in probabilistic language and to quantum statisti cal dynamics in terms of derivations. The Institute took place at the Center for Inter disciplinary Research of the University of Bielefeld. On behalf of all participants, it is a pleasure to thank the officials and the administration of the Center for their cooperation and help before and during the Insti tute. Special thanks go to V.C. Fulland, M. Kamper, and A. Kottenkamp for their rapid and competent preparation of the manuscripts.
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 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 National Research Symposium on Geometric Analysis and Applications ANU June 26 30 2000 written by Alexander Isaev and published by . This book was released on 2001 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceeding of the National Research Symposium on Geometric Analysis and Applications held at the Centre for Mathematics and its Applications, Australian National University, Canberra, from June 26-30, 2000. The Symposium celebrated the many significant contributions of Professor Derek W.
Download or read book Frustrated Spin Systems written by Hung-the Diep and published by World Scientific. This book was released on 2005-01-19 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frustrated spin systems have been first investigated five decades ago. Well-known examples include the Ising model on the antiferromagnetic triangular lattice studied by G H Wannier in 1950 and the Heisenberg helical structure discovered independently by A Yoshimori, J Villain and T A Kaplan in 1959. However, many properties of frustrated systems are still not well understood at present. Recent studies reveal that established theories, numerical simulations as well as experimental techniques have encountered many difficulties in dealing with frustrated systems. This volume highlights the latest theoretical, numerical and experimental developments in the field.The book is intended for post-graduate 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 formulae and full arguments leading to important results are given.
Download or read book Rigorous Results In Quantum Dynamics Proceedings Of The Conference written by Dittrich Jaroslav and published by #N/A. This book was released on 1991-07-22 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the conference is devoted mainly to the mathematically rigorous approaches to the problems of quantum mechanics. The spectral properties of Schrödinger operators, including those on regions with a boundary and their generalizations, scattering theory and resonances, time-dependent Hamiltonians and quantum chaos, problems of statistical physics like spin systems, and others are discussed.
Download or read book A Perturbative Approach to Quantum Propagation in Many body and Spin Systems with Confinement written by Dominik Bauernfeind and published by . This book was released on 2008 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stable Properties of Gapped Ground State Phases in Quantum Spin Chains written by Alvin S. Moon and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents three peer-reviewed journal articles on the topic of stable properties of gapped ground state phases of quantum spin systems, primarily in one dimension. Mathematical preliminaries for these papers are found in Chapter 1. A detailed summary of results, including main results, co-author information and funding acknowledgments, is found in Chapter 2. The Appendix comments on the hypotheses of the main result of Chapter 5.
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.
