Topology in Ordered Phases
Topology in Ordered Phases

Author: Satoshi Tanda

Publisher: World Scientific

Published: 2006

Total Pages: 392

ISBN-13: 9812772871

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The concept of topology has become commonplace in various scientific fields. The next stage is to bring together the knowledge accumulated in these fields. This volume contains articles on experiments and theories in connection with topology, including wide-ranging fields such as materials science, superconductivity, charge density waves, superfluidity, optics, and field theory. The nearly 60 peer-reviewed papers include contributions by noted authors Michael V Berry and Roman W Jackiw. The book serves as an excellent reference for both researchers and graduate students. Sample Chapter(s). Chapter 1: Optical Vorticulture (90 KB). Contents: Topology as a Universal Concept; Topological Crystals; Topological Materials; Topological Defects and Excitations; Topology in Quantum Phenomena; Topology in Optics; Topology in Quantum Device. Readership: Researchers and graduate students in materials science, condensed matter physics, optics, astrophysics and polymer science.

Topological Phases of Matter
Topological Phases of Matter

Author: Roderich Moessner

Publisher: Cambridge University Press

Published: 2021-04-29

Total Pages: 393

ISBN-13: 1107105536

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This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.

Topology in Condensed Matter
Topology in Condensed Matter

Author: Michael I. Monastyrsky

Publisher: Springer Science & Business Media

Published: 2006-02-04

Total Pages: 263

ISBN-13: 3540312641

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This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Topological Orders with Spins and Fermions
Topological Orders with Spins and Fermions

Author: Laura Ortiz Martín

Publisher: Springer

Published: 2019-07-11

Total Pages: 176

ISBN-13: 3030236498

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This thesis deals with topological orders from two different perspectives: from a condensed matter point of view, where topological orders are considered as breakthrough phases of matter; and from the emerging realm of quantum computation, where topological quantum codes are considered the most appealing platform against decoherence. The thesis reports remarkable studies from both sides. It thoroughly investigates a topological order called the double semion model, a counterpart of the Kitaev model but exhibiting richer quasiparticles as excitations. A new model for symmetry enriched topological order is constructed, which adds an onsite global symmetry to the double semion model. Using this topological phase, a new example of topological code is developed, the semion code, which is non-CSS, additive, non-Pauli and within the stabiliser formalism. Furthermore, the thesis analyses the Rashba spin-orbit coupling within topological insulators, turning the helical edge states into generic edges modes with potential application in spinstronics. New types of topological superconductors are proposed and the novel properties of the correspondingly created Majorana fermions are investigated. These Majorana fermions have inherent properties enabling braiding and the performance of logical gates as fundamental blocks for a universsal quantum computator.

Topological Phases of Matter
Topological Phases of Matter

Author: Roderich Moessner

Publisher: Cambridge University Press

Published: 2021-04-29

Total Pages: 393

ISBN-13: 1009038699

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Topological Phases of Matter are an exceptionally dynamic field of research: several of the most exciting recent experimental discoveries and conceptual advances in modern physics have originated in this field. These have generated new, topological, notions of order, interactions and excitations. This text provides an accessible, unified and comprehensive introduction to the phenomena surrounding topological matter, with detailed expositions of the underlying theoretical tools and conceptual framework, alongside accounts of the central experimental breakthroughs. Among the systems covered are topological insulators, magnets, semimetals, and superconductors. The emergence of new particles with remarkable properties such as fractional charge and statistics is discussed alongside possible applications such as fault-tolerant topological quantum computing. Suitable as a textbook for graduate or advanced undergraduate students, or as a reference for more experienced researchers, the book assumes little prior background, providing self-contained introductions to topics as varied as phase transitions, superconductivity, and localisation.

Topological Phases of Matter and Quantum Computation
Topological Phases of Matter and Quantum Computation

Author: Paul Bruillard

Publisher: American Mathematical Soc.

Published: 2020-03-31

Total Pages: 240

ISBN-13: 1470440741

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This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24–25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topics that nowadays are fundamental tools for the study of topological quantum computation. Moreover, the practical importance of this discipline has been underscored by recent industry investments. The relative youth of this field combined with a high degree of interest in it makes now an excellent time to get involved. Furthermore, the cross-disciplinary nature of topological quantum computing provides an unprecedented number of opportunities for cross-pollination of mathematics, physics, and computer science. This can be seen in the variety of works contained in this volume. With articles coming from mathematics, physics, and computer science, this volume aims to provide a taste of different sub-disciplines for novices and a wealth of new perspectives for veteran researchers. Regardless of your point of entry into topological quantum computing or your experience level, this volume has something for you.

Introduction to Topological Quantum Matter & Quantum Computation
Introduction to Topological Quantum Matter & Quantum Computation

Author: Tudor D. Stanescu

Publisher: CRC Press

Published: 2016-12-19

Total Pages: 395

ISBN-13: 1482245949

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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, 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.

Topological Quantum Matter
Topological Quantum Matter

Author: Thomas Klein Kvorning

Publisher: Springer

Published: 2018-08-12

Total Pages: 89

ISBN-13: 3319967649

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This book offers a theoretical description of topological matter in terms of effective field theories, and in particular topological field theories, focusing on two main topics: topological superconductors and topological insulators. Even though there is vast literature on these subjects, the book fills an important gap by providing a concise introduction to both topological order and symmetry-protected phases using a modern mathematical language, and developing the theoretical concepts by highlighting the physics and the physical properties of the systems. Further, it discusses in detail the topological interactions for topologically ordered matter, and the response to smooth external fields for symmetry protected matter. The book also covers more specialized topics that cannot be found elsewhere. Specifically, the response of superconductors to geometry, including the newly discovered geo-Meissner effect; and a correction to the usual Meissner effect, only present in the topologically interesting chiral superconductors.

Understanding Quantum Phase Transitions
Understanding Quantum Phase Transitions

Author: Lincoln Carr

Publisher: CRC Press

Published: 2010-11-02

Total Pages: 754

ISBN-13: 1439802610

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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

Topological Aspects of Condensed Matter Physics
Topological Aspects of Condensed Matter Physics

Author: Claudio Chamon

Publisher: Oxford University Press

Published: 2017

Total Pages: 705

ISBN-13: 019878578X

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This book contains lecture notes by world experts on topological quantum phenomena, which are being developed at unprecedented rates in novel material systems.