Theoretical study of entanglement in quantum impurity systems

Abstract

We develop a method to compute the entanglement negativity between the impurity spin and its environment in spin-$1/2$ impurity problems, based on the boundary conformal field theory. Applying this method and using tensor network methods, we analyze thermal entanglement and its spatial profile, which is called the Kondo screening cloud, in exotic quantum impurity systems such as multichannel Kondo systems, two impurity systems, and pseudogap Kondo systems. At low temperature, we show the universal behavior that the entanglement exhibits a power-law thermal decay with fractional exponent. The exponent is determined by the scaling dimension of the boundary operator representing the impurity spin. We show that the screening cloud also has the universal power law structure with the same exponent. I find that distinct (non-)Fermi liquids coexist in the cloud, forming concentric shells centered at the impurity. Outer shells are suppressed one by one as temperature increases, and the remaining outermost shell determines the thermal non-Fermi liquid phase of the metal at that temperature. We propose how to observe the entanglement and the screening cloud structure, based on a recent experimental setup.