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What is'topological'about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid-state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation?Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture and emphasizing two major new paradigms in condensed matter physics – quantum topology and quantum information – this book is ideal for graduate students and researchers entering this field, as it allows for the fruitful transfer of ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and unveils the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the toric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems.Topological quantum computation is also presented using a broad perspective, which includes elements of classical and quantum information theory, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and key ideas underlying quantum computation with anyons. This new edition has been updated throughout, with exciting new discussions on crystalline topological phases, including higher-order topological insulators; gapless topological phases, including Weyl semimetals; periodically-driven topological insulators; and a discussion of axion electrodynamics in topological materials.Key Features:· Provides an accessible introduction to this exciting, cross-disciplinary area of research.· Fully updated throughout with new content on the latest result from the field.· Authored by an authority on the subject.Tudor Stanescu is a professor of Condensed Matter Theory at West Virginia University, USA. He received a B.S. in Physics from the University of Bucharest, Romania, in 1994 and a Ph.D. in Theoretical Physics from the University of Illinois at Urbana Champaign in 2002. He was a Postdoctoral Fellow at Rutgers University and at the University of Maryland from 2003 to 2009. He joined the Department of Physics and Astronomy at West Virginia University in Fall 2009. Prof. Stanescu's research interests encompass a variety of topics in theoretical condensed matter physics including topological insulators and superconductors, topological quantum computation, ultra-cold atom systems in optical lattices, and strongly correlated materials, such as, for example, cuprate high-temperature superconductors. His research uses a combination of analytical and numerical tools and focuses on understanding the emergence of exotic states of matter in solid state and cold atom structures, for example, topological superconducting phases that host Majorana zero modes, and on investigating the possibilities of exploiting these states as physical platforms for quantum computation.

This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

What is'topological'about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation?Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems.Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.

This book presents the proceedings of the course'Spectroscopy and Dynamics of Collective Excitations in Solids'held in Erice, Italy from June 17 to July 1, 1995. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the'Ettore Majorana'Centre for Scientific Culture. The purpose of this course was to present and discuss physical models, mathematical formalisms, experimental techniques and applications relevant to the subject of collective excitations in solids. By bringing together specialists in the field of solid state spectroscopy, this course provided a much needed forum for the critical assessment and evaluation of recent and past developments in the physics of solids. A total of 83 participants came from 57 laboratories and 20 different countries (Austria, Belgium, Brazil, Denmark, Finland, France, Germany, Greece, Israel, Italy, Japan, The Netherlands, Norway, Portugal, Russia, Spain, Switzerland, Turkey, the United Kingdom, and the United States). The secretaries of the course were Stamatios K yrkos and Daniel Di Bartolo. 45 lectures divided in 13 series were given. In addition 8 (one or two-hour)'long seminars,'1'special lecture,'2 interdisciplinary lectures, 29'short seminars,'and 16 posters were presented. The sequence of lectures was in accordance with the logical development of the subject of the meeting. Each lecturer started at a rather fundamental level and ultimately reached the frontier of knowledge in the field.

This book presents an account of the course'Optical Properties of Excited States in Solids'held in Erice, Italy, from June 16 to 3D, 1991. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the'Ettore Majorana'Centre for Scientific Culture. The purpose of this course was to present physical models, mathematical formalisms and experimental techniques relevant to the optical properties of excited states in solids. Some active physical species, such as ions or radicals, could survive indefinitely if they were completely'isolated in space. Other active species, such as excited molecular and solid-state systems, are inherently unstable, even in isolation, due to the spontaneous mechanisms that may convert their excitation energies into radiation or heat. Physical parameters that may be used to characterize these excited systems are the localization or delocalization, and the coherence or incoherence, of their state excitations. In solids the excited states, whether they are localized (as for impurities in insulators) or delocalized (as they may occur in semiconductors), are relevant in several regards. Their de-excitation is extremely sensitive to the nature of the excitations of the systems, and a study of the de-excitation processes can yield a variety of information. For example, the excited states may represent the initial condition of the onset of such processes as Stokes-shifted emission, hot luminescence, symmetry-dependent Jahn-Teller and scattering processes, tunneling processes, energy transfer to like and unlike centers, superradiance, coherent radiation, and excited state absorption.

This unique volume presents the scientific achievements of outstanding scientists from different countries working in diverse areas of Condensed Matter Physics. Drawn from the 32nd International Workshop on Condensed Matter Theories held in Loughborough in August 2008, these 46 papers, while centered on the concepts and techniques of theoretical condensed matter physics, also address broad issues of common concern for all physicists. It is particularly relevant to theorists who apply advanced many-particle methods in other areas of physics.The primary topics covered in the paper contributions include: statistical mechanics, nonlinear dynamics, quantum Fermi and Bose liquids, boson condensates, strongly correlated electron systems, superconductivity and phase transitions. Among the specific questions addressed and discussed are modern theories of graphene, Quantum Hall Effect, models of social dynamics, which are based on the example of Obama-McCain election, extraordinary magnetoresistance, supercooled atomic gases, transitions between various magnetic states in different systems made from magnetic nanoparticles, order-disorder-order phase transitions in spin frustrated systems, embolic stroke and semifluxon dynamics in extended Josephson junctions. The book provides the latest updated information on modern Condensed Matter Theories and the methods used. The many recent developments in the field such as the discovery of graphene or of new phenomena in supercooled gases or of an extraordinary magnetoresistance augur well for this timely publication. The main value of the book lies in the diversity of topics being covered comprehensively, which puts the book in a primary position in the modern market.

Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit

Quantum many-body theory has greatly expanded its scope and depth over the past few years, treating more deeply long-standing issues like phase transitions and strongly-correlated systems, and simultaneously expanding into new areas such as cold atom physics and quantum information. This collection of contributions highlights recent advances in all these areas by leaders in their respective fields. Also included are some historic perspectives by L P Gor'kov and S T Belyaev, Feenberg Medal Recipients at this conference, and Nobel Laureate P W Anderson gives his unique outlook on the future of physics.The volume covers the key topics in many-body theory, tied together through advances in theoretical tools and computational techniques, and a unifying theme of fundamental approaches to quantum many-body physics.