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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
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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.

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:

Related Experiment Videos

  • 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.