DMRG simulation of spin chain three-channel Kondo model

The nontrivial low-temperature thermal impurity entropy in the electronic multichannel Kondo model reflects the existence and quantum dimension of anyons. For the open boundary condition (OBC) and periodic boundary condition (PBC) $J_1$-$J_2$ spin chain, the ground-state impurity entanglement entropy matches the thermal impurity entropy of the electronic one-channel and two-channel Kondo models, respectively. However, simulations of the one- and two-channel Kondo models using OBC and PBC in the $J_1$-$J_2$ spin chain lack generality, suggesting that the observed impurity entropy may be coincidental—unless more exotic impurity entropy, such as $\ln[(\sqrt{5}+1)/2]$ for the three-channel Kondo (3CK) model, can be realized. In this paper, we demonstrate that the correct boundary condition is the image impurity boundary condition (IIBC), which yields the expected impurity entropy, while the boundary condition that naturally extends PBC does not. Moreover, the IIBC reduces to OBC for the one-channel case and to PBC for the two-channel case.