Entanglement entropy in a boundary impurity model

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 or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaS(imp)) to the logarithmic entanglement entropy (S(ent)proportional tolnL/epsilon) scales as deltaS(imp)similar toy(r)lnL/epsilon, where y(r) is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaS(imp) diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.