nLab Quantum Information Meets Quantum Matter

This page compiles material related to the textbook:

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

  
  

  Quantum Information Meets Quantum Matter

  From Quantum Entanglement to Topological Phases of Many-Body Systems

  
  

  Quantum Science and Technology (QST)

  Springer (2019)

  arXiv:1508.02595

  doi:10.1007/978-1-4939-9084-9

on topological phases of matter/topological order characterized via concepts from quantum information theory, such as short- or long-range (topological) entanglement entropy.

Part I – Basic concepts in quantum information theory

• quantum information theory

Sec. 1 – Correlation and Entanglement

• entanglement

Sec. 2 –Evolution of Quantum Systems

• quantum system

• quantum mechanics

Sec. 3 – Quantum Error Correcting Codes

• quantum error correcting code

Part II – Local Hamiltonians, Ground States, and Many-Body Entanglement

• Hamiltonian

• ground state

Sec. 4 – Local Hamiltonians and Ground States

Sec. 5 – Gapped Quantum Systems and Entanglement Area Law

• topological insulator

• holographic entanglement entropy

• topological entanglement entropy

Part III – Topological Order and Long-Range Entanglement

Sec. 6 – Introduction to Topological Order

• topological phases of matter

• topological order

• string-net

• string-net model

Sec. 7 – Local Transformations and Long-Range Entanglement

• long-range entanglement

Part IV – Gapped Topological Phases and Tensor Networks

• tensor network

Sec. 8 – Matrix Product States and 1D Gapped Phases

• matrix product state

Sec. 9 – Tensor Product States and 2d Gapped Phases

Sec. 10 – Symmetry Protected Topological Phases

• symmetry protected topological phase

Part V – Outlook

Sec. 11 – A Unification of Information and Matter

• string-net theory?

• string-net liquid?

• string-net condensation?

… an article should be made about the string-net description of gauge theory, as detailed in this chapter.

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category: reference