Entanglement entropy in a boundary impurity model

TL;DR

This paper calculates how a boundary impurity affects the entanglement entropy in a 1+1 dimensional Luttinger liquid, revealing a divergence in the entropy correction and supporting the idea of entropy decrease along RG flow.

Contribution

It introduces a novel finite size scaling and bosonization approach to compute impurity effects on entanglement entropy in Luttinger liquids.

Findings

Boundary impurity correction scales as y ln(L/e)

In the repulsive case, the correction diverges negatively

Results support the irreversibility of entanglement entropy decrease along RG flow

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 (\delta S) to the bulk logarithmic entanglement entropy (S_{ent} ~ ln(L/e)) scales as \delta S ~ 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), \delta S 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.