Quantum entanglement in the kondo effect at finite temperature

Abstract

The Kondo effect is a phenomenon in quantum impurity systems, which introduces the quantum entanglement between a magnetic impurity and free electron channels as a temperature decreases. The Kondo effect is a prototype of many-body correlated phenomena, and is the one of the central subjects of condensed matter physics. Although the Kondo effect has been studied extensively at finite temperature, its quantum entanglement has not been computed exactly at finite temperature. In this dissertation, we perform the three studies to understand the quantum entanglement in the Kondo effect at finite temperature. First, we develop a numerical method to compute the quantum entanglement between the impurity and the channels at finite temperature. We use entanglement negativity to quantify the quantum entanglement and use numerical renormalization group to solve the quantum impurity systems. Second, we study the quantum entanglement in the single-channel Kondo effect. We find that both the spin and the charge degrees of freedom of the impurity contribute to the quantum entanglement, and the quantum entanglement contributed from the spin shows a universal power law scaling in temperature. Third, we study the quantum entanglement in the two-channel Kondo effect. We find that the quantum entanglement shows a power law scaling in temperature with the scaling exponent depending on the kind of the Kondo fixed point, and indicates the thermal crossover between the different Kondo fixed points. Also, we check the correspondence between the two-channel Kondo and the two-impurity Kondo by the quantum entanglement at finite temperature.