Entanglement in quantum impurity problems is non perturbative

Abstract

We study the entanglement entropy of a region of length 2L with the remainder of an infinite one dimensional gapless quantum system in the case where the region is centered on a quantum impurity. The coupling to this impurity is not scale invariant, and the physics involves a crossover between weak and strong coupling regimes. While the impurity contribution to the entanglement has been computed numerically in the past, little is known analytically about it, since in particular the methods of conformal invariance cannot be applied because of the presence of a crossover length. We show in this paper that the small coupling expansion of the entanglement entropy in this problem is quite generally plagued by strong infrared divergences, implying a non-perturbative dependence on the coupling. The large coupling expansion turns out to be better behaved, thanks to powerful results from the boundary CFT formulation and, in some cases, the underlying integrability of the problem. However, it is clear that this expansion does not capture well the crossover physics. In the integrable case -- which includes problems such as an XXZ chain with a modified link, the interacting resonant level model or the anisotropic Kondo model -- a non perturbative approach is in principle possible using form-factors. We adapt in this paper the ideas of [1,2] to the gapless case and show that, in the rather simple case of the resonant level model, and after some additional renormalizations, the form factors approach yields remarkably accurate results for the entanglement all the way from short to large distances. This is confirmed by detailed comparison with numerical simulations. Both our form factor and numerical results are compatible with a non-perturbative form at short distance.

18 pages, 4 figures. v3: minor post-publication footnote added

References in corpus (6)

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• Universal and measurable entanglement entropy in the spin-boson model
• Strong enhancement of transport by interaction on contact links
• Impurity Entanglement Entropy and the Kondo Screening Cloud
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Cited by in corpus (19)

• Quantum entanglement in condensed matter systems
• Energy transport between two integrable spin chains
• Universal entanglement crossover of coupled quantum wires
• Long-range entanglement near a Kondo-destruction quantum critical point
• Real-space structure of the impurity screening cloud in the Resonant Level Model
• Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class
• Exact equilibrium results in the Interacting Resonant Level Model
• Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization
• Dynamics of the impurity screening cloud following quantum quenches of the Resonant Level Model
• Universal Entanglement Dynamics following a Local Quench
• Single-impurity Kondo physics at extreme particle-hole asymmetry
• Quantum Renyi relative entropies on a spin chain with interface defects
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state
• Quantum entanglement in a pure state of strongly correlated quantum impurity systems
• Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
• Entanglement Entropy in Integrable Field Theories with Line Defects I. Topological Defect
• Local density of states of the interacting resonant level model at zero temperature
• Entanglement flow in the Kane-Fisher quantum impurity problem
• Entanglement Entropy in Integrable Field Theories with Line Defects II. Non-topological Defect