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 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, $\ln (g_{UV}/g_{IR})=\ln(2)/2$, 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 $\xi_{2CK}$. 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, $\nu\!\approx\! 2$ and $\beta \!\approx\! 0.2$. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.

Entanglement structure of the two-channel Kondo model Journal Articles