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Quantum Information Meets Quantum Matter

From Quantum Entanglement to Topological Phases of Many-Body Systems

  • Bei Zeng
  • Xie Chen
  • Duan-Lu Zhou
  • Xiao-Gang Wen
Book

Part of the Quantum Science and Technology book series (QST)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Basic Concepts in Quantum Information Theory

    1. Front Matter
      Pages 1-1
    2. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 3-35
    3. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 37-61
    4. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 63-82
  3. Local Hamiltonians, Ground States, and Many-Body Entanglement

    1. Front Matter
      Pages 83-83
    2. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 85-113
    3. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 115-153
  4. Topological Order and Long-Range Entanglement

    1. Front Matter
      Pages 155-155
    2. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 157-189
    3. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 191-229
  5. Gapped Topological Phases and Tensor Networks

    1. Front Matter
      Pages 231-231
    2. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 233-253
    3. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 255-279
    4. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 281-332
  6. Outlook

    1. Front Matter
      Pages 333-333
    2. Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
      Pages 335-364

About this book

Introduction

This book approaches condensed matter physics from the perspective of quantum information science, focusing on systems with strong interaction and unconventional order for which the usual condensed matter methods like the Landau paradigm or the free fermion framework break down. Concepts and tools in quantum information science such as entanglement, quantum circuits, and the tensor network representation prove to be highly useful in studying such systems. The goal of this book is to introduce these techniques and show how they lead to a new systematic way of characterizing and classifying quantum phases in condensed matter systems.

The first part of the book introduces some basic concepts in quantum information theory which are then used to study the central topic explained in Part II: local Hamiltonians and their ground states. Part III focuses on one of the major new phenomena in strongly interacting systems, the topological order, and shows how it can essentially be defined and characterized in terms of entanglement.  Part IV shows that the key entanglement structure of topological states can be captured using the tensor network representation, which provides a powerful tool in the classification of quantum phases. Finally, Part V discusses the exciting prospect at the intersection of quantum information and condensed matter physics – the unification of information and matter.

Intended for graduate students and researchers in condensed matter physics, quantum information science and related fields, the book is self-contained and no prior knowledge of these topics is assumed.

Keywords

boson/spin liquids entanglement in many-body systems gapped quantum phases quantum entanglement quantum information and condensed matter physics quantum many-body physics quantum order tensor network topological order

Authors and affiliations

  • Bei Zeng
    • 1
  • Xie Chen
    • 2
  • Duan-Lu Zhou
    • 3
  • Xiao-Gang Wen
    • 4
  1. 1.University of GuelphGuelphCanada
  2. 2.PhysicsCalifornia Institute of TechnologyPasadenaUSA
  3. 3.Institute of PhysicsChinese Academy of SciencesBeijingChina
  4. 4.Massachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-9084-9
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2019
  • Publisher Name Springer, New York, NY
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-1-4939-9082-5
  • Online ISBN 978-1-4939-9084-9
  • Series Print ISSN 2364-9054
  • Series Online ISSN 2364-9062
  • Buy this book on publisher's site