title: Universal entanglement crossover of coupled quantum wires.
abstract: We consider the entanglement between two one-dimensional quantum wires (Luttinger liquids) coupled by tunneling through a quantum impurity. The physics of the system involves a crossover between weak and strong coupling regimes characterized by an energy scale TB, and methods of conformal field theory therefore cannot be applied. The evolution of the entanglement in this crossover has led to many numerical studies, but has remained little understood, analytically or even qualitatively. We argue in this Letter that the correct universal scaling form of the entanglement entropy S (for an arbitrary interval of length L containing the impurity) is ∂S/∂ ln L=f(LTB). In the special case where the coupling to the impurity can be refermionized, we show how the universal function f(LTB) can be obtained analytically using recent results on form factors of twist fields and a defect massless-scattering formalism. Our results are carefully checked against numerical simulations.
authors.affiliation: Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Romain
authors.initials: R
authors.lastname: Vasseur
authors.affiliation: LPTENS, 24 rue Lhomond, 75231 Paris, France and Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France.
authors.forename: Jesper Lykke
authors.initials: JL
authors.lastname: Jacobsen
authors.affiliation: Institut de Physique Théorique, CEA Saclay, 91191 Gif Sur Yvette, France and Department of Physics, University of Southern California, Los Angeles, California 90089-0484, USA.
authors.forename: Hubert
authors.initials: H
authors.lastname: Saleur