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Detecting topological order in a ground state wave function.

Michael Levin1, Xiao-Gang Wen

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|April 12, 2006
PubMed
Summary
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Researchers can detect topological orders using the ground state wave function. This method computes topological entropy, which measures the total quantum dimension of these complex quantum states.

Area of Science:

  • Condensed matter physics
  • Quantum information theory
  • Topological phases of matter

Background:

  • Topological orders are a key concept in modern physics, describing exotic states of matter.
  • The string-net condensation picture provides a framework for understanding and classifying these orders.
  • Characterization typically involves complex data sets like (N, di, F(lmn)(ijk), delta(ijk).

Purpose of the Study:

  • To develop a method for detecting topological orders directly from the ground state wave function.
  • To establish a practical approach for identifying these complex quantum states without relying on extensive theoretical data.
  • To connect the physical properties of topological orders to measurable quantities.

Main Methods:

  • Utilizing the ground state wave function as the sole input.

Related Experiment Videos

  • Computing a specific quantity known as topological entropy.
  • Relating topological entropy to the total quantum dimension (D = Sum(di^2)).

    • Main Results:

    • A novel method is presented to detect topological orders.
    • Topological entropy is identified as a direct and computable measure of topological order.
    • The total quantum dimension can be directly extracted from the ground state wave function.

    Conclusions:

    • The ground state wave function contains sufficient information to detect and characterize topological orders.
    • Topological entropy offers a powerful and practical tool for identifying these states in physical systems.
    • This work simplifies the detection of topological orders, making them more accessible for experimental and theoretical study.