Abstract
In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the Interacting Resonant Level Model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results for the Kondo model to describe the infrared fixed point, conformal field theory techniques initially developed by Cardy and Calabrese and a quantization scheme that allows one to compute exactly Renyi entropies at arbitrary order in 1/TB in principle, even when the system size or the temperature is finite. We show that those universal quantities at arbitrary interaction parameter in the strong coupling regime are very well approximated by the same quantities in the free fermion system in the case of attractive Coulomb interaction, whereas a strong dependence on the interaction appears in the case of repulsive interaction.
Highlights
Entanglement is a property allowed by quantum mechanics that describes the fact that generically, a quantum state of a system consisting of several subparts cannot be written as a product of states of the subparts
In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the interacting resonant level model (IRLM), at low energy
In 1+1 dimensional many-body systems at their critical point described by a CFT, it has been shown that the replica method allows for a computation of the Renyi and the entanglement entropies
Summary
Entanglement is a property allowed by quantum mechanics that describes the fact that generically, a quantum state of a system consisting of several subparts cannot be written as a product of states of the subparts. In the integrable case, the existence of an infinity of conserved quantities does, provide a full control of the low energy hamiltonian: the necessarily infinite number of counter terms are all explicitly known [24], together with a well defined (analytical) regularization procedure This means that, while we do not know how to calculate the scaling functions at small coupling (since they are not perturbative), we have, in principle, a tool to determine them perturbatively at large coupling.
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