3 edition of **Topological phases in quantum theory** found in the catalog.

- 41 Want to read
- 28 Currently reading

Published
**1989**
by World Scientific in Singapore, Teaneck, NJ
.

Written in English

- Quantum theory -- Congresses.,
- Topology -- Congresses.,
- Geometrical optics -- Congresses.,
- Geometry, Differential -- Congresses.

**Edition Notes**

...

Statement | editors, B. Markovski, S.I. Vinitsky. |

Contributions | Markovski, B., Vinitsky, S. I. |

Classifications | |
---|---|

LC Classifications | QC173.96 .T66 1989, QC173.96 .T66 1989 |

The Physical Object | |

Pagination | viii, 455 p. : |

Number of Pages | 455 |

ID Numbers | |

Open Library | OL17969954M |

ISBN 10 | 997150877X |

LC Control Number | 89022511 |

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic algebraic topology, and have some basic background in quantum field theory. topological quantum ﬂeld theory and quantum computing. In quantum computing, the application of topology is most interesting because the simplest non-trivial example of the Temperley{Lieb recoupling Theory gives the so-called Fibonacci model. The recoupling theory yields rep-resentations of the Artin braid group into unitary groups U(n) where.

Topological Quantum Information Theory. topological quantum ﬁeld theory and quantum computing. phases as corresponding to the interchange of the particles labeled a and b in. Oct 07, · As a result, the spins throughout the 2D material are able to align with each other to a certain degree. This alignment is a form of “topological order” that also applies more generally to 2D systems of atoms (or electrons) that align an aspect of their Author: Michael Schirber.

Nov 20, · This builds a framework that allows us to look at the theory of a new concept, called quantum entanglement, which serves as a fundamental object that we use to develop new theories for topological phase of matter later in this cie-du-scenographe.com by: This course will cover current developments on topological phases in condensed matter physics, including: the theory of the fractional quantum Hall states, spin liquids, topological insulators and superconductors, effective field theories of topological phases, quasiparticles, fractional statistics (Abelian and non-Abelian), experimental.

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Topological Quantum: Lecture Notes S. Simon Michaelmas I’m not sure if these notes will become a book or not. In some ways the notes for a course are not necessarily the right outline for making a good book.

Topological Quantum page 2. 6 Topological Quantum Field Theory A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.

Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry.

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states.

Microscopically, topological orders correspond to patterns of long-range quantum entanglement. networks, and symmetry-protected topological phases. Structure of the Book The book has ﬁve parts, each includes several chapters.

We start from Part I for introducing the basic concepts in quantum information that will be later used in the book. Quantum information science is a very large ﬁeld and many new ideas and concepts are developed. This book provides a systematic approach to the study of condensed matter physics from the perspective of quantum information science, beginning with the basic concepts, developing tools used in quantum information theory and applying them to the study of many body systems.

Buy Quantum Information Meets Quantum Matter: From Quantum Entanglement to Topological Phases of Many-Body Systems (Quantum Science and Technology) Cited by: 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 Cited by: 8. A very nice book is from Kauffman called Knots and Physics. Also the book by Baez and Munaiin has two introductory chapters on Chern-Simons theory and its relation to link invariants.

There are also some physical applications of Chern-Simons Theory. For instance, it appears as an effective (longe wavelength) theory of the fractional quantum.

Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories.

In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian cie-du-scenographe.com by: Note: Citations are based on reference standards.

However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.

This book covers basic and advanced aspects in the field of Topological Matter. The chapters are based on the lectures presented during the Topological Matter School It provides graduate level content introducing the basic concepts of the field, including an introductory session on group theory and topological classification of matter.

What are topological phases of matter. First, they are phases of matter at zero temperature. Second, they have a non-zero energy gap. Third, they are more complicated and subtle than the familiar.

Dec 07, · "In the last twenty years, several themes have come to the forefront of quantum condensed matter physics research through cross-fertilization with other disciplines, such as: topological matter and its emergent quasiparticles, quantum information theory, and quantum computation.4/5(2).

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.

"Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories.

In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. 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. "This book is a sort of travel guide through topological quantum computation [it] is composed of four parts, preliminaries that introduce quantum mechanics, part two that deals with topological phases of matter and part three that deals with theories of topological quantum matter.

Dec 24, · Thus, the topological order was introduced to characterize the superfluid phases. The topological aspects in these two phases have been discussed in detail in the book by Volovik.

Some concepts and topological invariants can be applied explicitly to topological insulators in the framework of a single-particle wave function in the band cie-du-scenographe.com by: 3. Dec 19, · Introduction to Topological Quantum Matter & Quantum Computation book.

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.

and elements of Cited by: 8. Foundations of Topological Order: Quantum Topological States of Matter with Applications in Solid State Physics, Quantum Computing, and Quantum Information Theory A White Paper on Applications of M. Epperson, E.

Zafiris, Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature. Lexington Books. Apr 22, · Abstract. Role of topology in generating exotic topological phases of quantum matter is discussed. Illustrative examples of 2D quantum spin-Hall insulators, 3D topological insulators, topological crystalline insulators, and topological Weyl and Dirac semi-metals are cie-du-scenographe.com: Wei-Feng Tsai, Hsin Lin, Arun Bansil.Abstract: This is a collection of lecture notes from three lectures given by Alexei Kitaev at the Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a pedagogical introduction to topological phenomena in 1-D superconductors and in the 2-D topological phases of the toric code and honeycomb cie-du-scenographe.com by: Apr 21, · Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories.

In this approach, information is stored in the lowest energy states of many-anyon systems and processed by .