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 $T_B$, 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 $\partial S/\partial \ln L=f(L{T}_B)$. In the special case where the coupling to the impurity can be refermionized, we show how the universal function $f(L{T}_B)$ 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.

v2: to appear in PRL

References in corpus (5)

• Solution of the fermionic entanglement problem with interface defects
• Crossover physics in the non-equilibrium dynamics of quenched quantum impurity systems
• Impurity Entanglement Entropy and the Kondo Screening Cloud
• Entanglement in quantum impurity problems is non perturbative
• Impurity entanglement entropy in Kondo systems from conformal field theory

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• Exact overlaps in the Kondo problem
• Universal entanglement signatures of interface conformal field theories
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• Universal Entanglement Dynamics following a Local Quench
• Healing of Defects in Random Antiferromagnetic Spin Chains
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Kane-Fisher weak link physics in the clean scratched-XY model
• Entanglement flow in the Kane-Fisher quantum impurity problem