2004/08/31 by Greg Levine, Gregory Levine
Physics and Astronomy · #Bosonization #Condensed matter physics #Entropy (arrow of time) #Fermion #Impurity #Logarithm #Luttinger liquid #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Scaling #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevlett.93.266402
published as Phys. Rev. Lett. 93, 266402 (2004) · 5 pages, 2 figures; to appear in Phys. Rev. Lett
arxiv created 2004/11/30 · openalex publication_date 2004/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ϵ, the boundary impurity correction (\ensuremathδSimp) to the logarithmic entanglement entropy (Sent\ensuremath∝lnL/ϵ) scales as \ensuremathδSimp\ensuremath∼yrlnL/ϵ, 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), \ensuremathδSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.