Entanglement structure of the two-channel Kondo model
Two electronic channels competing to screen a single impurity spin, as in the two-channel Kondo model, are expected to generate a ground state with a nontrivial entanglement structure. We exploit a spin-chain representation of the two-channel Kondo model to probe the ground-state block entropy, negativity, tangle, and Schmidt gap, using a density matrix renormalization group approach. In the presence of symmetric coupling to the two channels, we confirm field-theory predictions for the boundary entropy difference $ln({g}_{\text{UV}}/{g}_{\text{IR}})=ln(2)/2$ between the ultraviolet and infrared limits and the leading $ln(x)/x$ impurity correction to the block entropy. The impurity entanglement ${S}_{\text{imp}}$ is shown to scale with the characteristic length ${\ensuremath{\xi}}_{2\text{CK}}$. We show that both the Schmidt gap and the entanglement of the impurity with one of the channels---as measured by the negativity---faithfully serve as order parameters for the impurity quantum phase transition appearing as a function of channel asymmetry, allowing for explicit determination of critical exponents, $\ensuremath{\nu}\ensuremath{\approx}2$ and $\ensuremath{\beta}\ensuremath{\approx}0.2$. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.