Quantum Ising Phases And Transitions In Transverse Ising Models

Quantum phase transitions, driven by quantum fluctuations, exhibit intriguing features offering the possibility of potentially new applications, e.g. in quantum information sciences. Major advances have been made in both theoretical and experimental investigations of the nature and behavior of quantum phases and transitions in cooperatively interacting many-body quantum systems. For modeling purposes, most of the current innovative and successful research in this field has been obtained by either directly or indirectly using the insights provided by quantum (or transverse field) Ising models because of the separability of the cooperative interaction from the tunable transverse field or tunneling term in the relevant Hamiltonian. Also, a number of condensed matter systems can be modeled accurately in this approach, hence granting the possibility to compare advanced models with actual experimental results. This work introduces these quantum Ising models and analyses them both theoretically and numerically in great detail. With its tutorial approach the book addresses above all young researchers who wish to enter the field and are in search of a suitable and self-contained text, yet it will also serve as a valuable reference work for all active researchers in this area.

This book establishes the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information.

Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.

"Discusses the recent developments in quantum statistical physics of spin glasses and quantum computations"--Provided by publisher.

Neutron Scattering - Magnetic and Quantum Phenomena provides detailed coverage of the application of neutron scattering in condensed matter research. The book's primary aim is to enable researchers in a particular area to identify the aspects of their work where neutron scattering techniques might contribute, conceive the important experiments to be done, assess what is required to carry them out, write a successful proposal for one of the major user facilities, and perform the experiments under the guidance of the appropriate instrument scientist. An earlier series edited by Kurt Sköld and David L. Price, and published in the 1980s by Academic Press as three volumes in the series Methods of Experimental Physics, was very successful and remained the standard reference in the field for several years. This present work has similar goals, taking into account the advances in experimental techniques over the past quarter-century, for example, neutron reflectivity and spin-echo spectroscopy, and techniques for probing the dynamics of complex materials of technological relevance. This volume complements Price and Fernandez-Alonso (Eds.), Neutron Scattering - Fundamentals published in November 2013. Covers the application of neutron scattering techniques in the study of quantum and magnetic phenomena, including superconductivity, multiferroics, and nanomagnetism Presents up-to-date reviews of recent results, aimed at enabling the reader to identify new opportunities and plan neutron scattering experiments in their own field Provides a good balance between theory and experimental techniques Provides a complement to Price and Fernandez-Alonso (Eds.), Neutron Scattering - Fundamentals published in November 2013

This book reviews some of the classic aspects in the theory of phase transitions and critical phenomena, which has a long history. Recently, these aspects are attracting much attention due to essential new contributions. The topics presented in this book include : mathematical theory of the Ising model; equilibrium and non-equilibrium criticality of one-dimensional quantum spin chains; influence of structural disorder on the critical behaviour of the Potts model; criticality, fractality and multifractality of linked polymers; field-theoretical approaches in the super conducting phase transitions. The book is based on the review lectures that were given in Lviv (Ukraine) in March 2002 at the "Ising lectures" - a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in the field of phase transitions with university students and those who are interested in the subject.

This book presents a new way of thinking about quantum mechanics and machine learning by merging the two. Quantum mechanics and machine learning may seem theoretically disparate, but their link becomes clear through the density matrix operator which can be readily approximated by neural network models, permitting a formulation of quantum physics in which physical observables can be computed via neural networks. As well as demonstrating the natural affinity of quantum physics and machine learning, this viewpoint opens rich possibilities in terms of computation, efficient hardware, and scalability. One can also obtain trainable models to optimize applications and fine-tune theories, such as approximation of the ground state in many body systems, and boosting quantum circuits’ performance. The book begins with the introduction of programming tools and basic concepts of machine learning, with necessary background material from quantum mechanics and quantum information also provided. This enables the basic building blocks, neural network models for vacuum states, to be introduced. The highlights that follow include: non-classical state representations, with squeezers and beam splitters used to implement the primary layers for quantum computing; boson sampling with neural network models; an overview of available quantum computing platforms, their models, and their programming; and neural network models as a variational ansatz for many-body Hamiltonian ground states with applications to Ising machines and solitons. The book emphasizes coding, with many open source examples in Python and TensorFlow, while MATLAB and Mathematica routines clarify and validate proofs. This book is essential reading for graduate students and researchers who want to develop both the requisite physics and coding knowledge to understand the rich interplay of quantum mechanics and machine learning.