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Quantum Information Meets Quantum Matter pp 115–153Cite as

Gapped Quantum Systems and Entanglement Area Law

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Abstract

We discuss quantum systems of large system size N, in particular, the \(N\rightarrow \infty \) limit (thermodynamic limit). We call them the quantum many-body systems. We ask about the physical properties of these quantum many-body systems in the thermodynamic limit. Our main focus in this chapter will be many-body systems with an energy gap and the entanglement properties of their ground states. We introduce the entanglement area law and its constant correction—the topological entanglement entropy. We discuss the information-theoretic meaning of topological entanglement entropy, and generalize it to construct a “universal entanglement detector”, whose values on the gapped ground states provide nontrivial information of the system.

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Author information

Authors and Affiliations

  1. University of Guelph, Guelph, ON, Canada

    Bei Zeng

  2. Physics, California Institute of Technology, Pasadena, CA, USA

    Xie Chen

  3. Institute of Physics, Chinese Academy of Sciences, Beijing, China

    Duan-Lu Zhou

  4. Massachusetts Institute of Technology, Cambridge, MA, USA

    Xiao-Gang Wen

Authors
  1. Bei Zeng
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  2. Xie Chen
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  3. Duan-Lu Zhou
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  4. Xiao-Gang Wen
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Corresponding author

Correspondence to Bei Zeng .

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Zeng, B., Chen, X., Zhou, DL., Wen, XG. (2019). Gapped Quantum Systems and Entanglement Area Law. In: Quantum Information Meets Quantum Matter. Quantum Science and Technology. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9084-9_5

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  • DOI: https://doi.org/10.1007/978-1-4939-9084-9_5

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-9082-5

  • Online ISBN: 978-1-4939-9084-9

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