For two free-fermion lattices connected by a few quantum point contacts, the entanglement entropy of typical excited eigenstates grows only linearly with subsystem size, not extensively.
Entanglement entropy in a boundary impurity model
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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.
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The Eigenstate Thermalization Hypothesis in a Quantum Point Contact Geometry
For two free-fermion lattices connected by a few quantum point contacts, the entanglement entropy of typical excited eigenstates grows only linearly with subsystem size, not extensively.