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 ∊, the boundary impurity correction (δSimp) to the logarithmic entanglement entropy (Sent∝ln(L/∊) scales as δSimp̃yrln(L/∊, where yr 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), δSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.
Physical Review Letters
- Pub Date:
- December 2004
- Theories and models of many-electron systems;
- Quantum information;
- Strongly Correlated Electrons
- 5 pages, 2 figures