Exploring Kondo effect by quantum energy teleportation

We consider a quantum energy teleportation (QET) method to replicate the phase diagram of a one-dimensional $XXZ$ spin chain featuring a Kondo effect coupling. In this setup, the energy supplier and receiver are spatially separated from the point impurity and do not interact directly with it. Nonetheless, they may successfully generate phase diagrams that closely mirror those produced via exact diagonalization. This can be achieved using only local operations on their respective subsystems, supplemented by classical communication. This feat is made possible due to a critical connection between the energy obtained through the QET approach and the system's quantum entanglement entropy. To substantiate these findings, we initially demonstrate that the quantum entanglement entropy serves as the relevant order parameter for the system. Intriguingly, changes in the gap spacing of the entanglement spectra align with the locations of peaks in both entanglement entropy and energy, as determined by QET. We hypothesize that this theoretical framework could, for example, be validated experimentally using a one-dimensional chain of Rydberg atoms.