Finite-coupling vanishing of the Fermi-liquid scale

Determine whether the Fermi-liquid crossover scale $T_{FL}$ in the two-site charge-Kondo model vanishes at finite inter-island coupling $t_C$ or merely becomes exceedingly small.

Background

The paper studies two coupled charge-Kondo islands, focusing in the Kondo limit on the Fermi-liquid crossover that emerges at sufficiently strong inter-island coupling tCt_C. The crossover scale TFLT_{FL} is defined through the impurity entropy and is numerically fitted to a Kondo-like form, TFL/D=bexp⁡(−1/(ctC))T_{FL}/D=b\exp(-1/(ct_C)).

Although the numerical results indicate a screened Fermi-liquid state at strong coupling, the available NRG data do not establish whether the fitted scale remains strictly positive for every finite tCt_C or approaches zero at a finite coupling. Resolving this behavior would clarify the phase structure and the possible existence of a finite-coupling boundary associated with the onset of Fermi-liquid screening.

References

We comment here that our NRG data alone cannot resolve whether $T_{FL}$ actually vanishes at finite $t_C$ or just becomes exceedingly small.

— Coupled quantum critical states in a circuit simulator  (2610.10048 - Karki et al., 7 Oct 2026) in End Matter, section “NRG implementation and observables”