Numerical renormalization group method for entanglement negativity at finite temperature

We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativit...

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Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Shim, Jeongmin, H -S Sim, Lee, Seung-Sup B
Format: Article
Language:English
Subjects:
Entanglement
High temperature
Impurities
Kondo temperature
Mathematical models
Numerical methods
Power law
Scaling
Variation
Online Access:Get full text
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Summary:We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contribute to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.
ISSN:2331-8422
DOI:10.48550/arxiv.1808.08506