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(gUV/gIR)=ln(2)/2 between the ultraviolet and infrared limits and the leading ln(x)/x impurity correction to the block entropy. The impurity entanglement Simp is shown to scale with the characteristic length ξ2CK. 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, ν≈2 and β≈0.2. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.