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Domain Wall Topological Entanglement Entropy.

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We found a universal correction to ground-state entanglement entropy in gapped domain walls between topologically ordered systems. This correction relates to the quantum dimension of superselection sectors on the domain wall.

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Area of Science:

  • Condensed matter physics
  • Quantum information theory
  • Topological order

Background:

  • Topologically ordered systems exhibit unique quantum phenomena.
  • Domain walls can host exotic quantum states.
  • Entanglement entropy quantifies quantum correlations.

Purpose of the Study:

  • To investigate the ground-state entanglement of domain walls in 2D topologically ordered systems.
  • To derive a universal formula for entanglement entropy corrections at domain walls.

Main Methods:

  • Utilizing the entanglement bootstrap method.
  • Analyzing gapped domain walls between topologically ordered phases.
  • Calculating ground-state entanglement entropy.

Main Results:

  • A universal correction to ground-state entanglement entropy was derived.
  • This correction is equal to the logarithm of the total quantum dimension of superselection sectors.
  • The derived formula applies to domain walls in two spatial dimensions.

Conclusions:

  • The entanglement structure of domain walls is universally characterized by quantum dimensions.
  • The entanglement bootstrap method provides a powerful tool for studying topological entanglement.
  • This work deepens the understanding of entanglement in topologically ordered systems.