Numerical renormalization group method for entanglement negativity at finite temperature

TL;DR

This paper introduces a numerical renormalization group method to compute entanglement negativity in quantum impurity systems at finite temperature, enabling analysis of entanglement dynamics in these complex systems.

Contribution

The authors develop a novel NRG-based approach to evaluate negativity in impurity-bath systems at finite temperature, including a computationally efficient approximation.

Findings

Negativity shows power-law scaling at low temperatures in the Kondo model.

Negativity exhibits sudden death at high temperatures.

Charge fluctuations affect negativity in the Anderson model even at zero temperature.

Abstract

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.