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Related Experiment Videos

Entanglement entropy in a boundary impurity model.

G C Levine1

  • 1Department of Physics and Astronomy, Hofstra University, Hempstead, New York 11549, USA.

Physical Review Letters
|February 9, 2005
PubMed
Summary

Boundary impurities significantly impact strongly correlated systems. This study reveals how impurity scattering affects entanglement entropy in Luttinger liquids, showing entropy can vanish due to boundary effects.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory

Background:

  • Boundary impurities profoundly influence bulk properties in (1+1)-dimensional strongly correlated systems.
  • Entanglement entropy is a key measure of quantum correlations in many-body systems.

Purpose of the Study:

  • To compute the entanglement entropy of a zero-temperature Luttinger liquid with a single boundary impurity.
  • To investigate the relationship between entanglement entropy and scattering properties at the boundary.

Main Methods:

  • A novel finite size scaling and bosonization scheme was employed.
  • The boundary impurity correction to entanglement entropy was calculated for a Luttinger liquid of finite length (2L) with a UV cutoff (epsilon).

Main Results:

  • The boundary impurity correction (deltaSimp) to logarithmic entanglement entropy (Sent) scales as deltaSimp ~ yr ln(L/epsilon), where yr is the renormalized backscattering coupling constant.
  • In the repulsive case (g<1), deltaSimp diverges negatively, indicating a vanishing entanglement entropy.
  • A direct link between entanglement entropy and boundary scattering was established.

Conclusions:

  • Entanglement entropy is shown to decrease irreversibly along renormalization group flow, consistent with recent conjectures.
  • Boundary impurities play a critical role in determining the entanglement properties of quantum systems.

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