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Entanglement entropy in a boundary impurity model

Gregory Levine
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Abstract

Boundary impurities are known to dramatically alter certain bulk properties of 1+1 dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling/bosonization scheme. For a Luttinger liquid of length 2L and UV cut off, e, the boundary impurity correction (δS) to the bulk logarithmic entanglement entropy (S_{ent} ~ ln(L/e)) scales as δS ~ y ln(L/e), where y is the renormalized impurity coupling constant. In this way, the bulk entanglement entropy within a region is related to scattering from the region's boundary. In the repulsive case (g<1), δS diverges (negatively) suggesting that the bulk entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

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Gregory Levine. 2004-11-30. Entanglement entropy in a boundary impurity model. https://doi.org/10.1103/physrevlett.93.266402

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