Coupled quantum critical states in a circuit simulator

Hybrid metal-semiconductor quantum circuits offer a controlled setting for realizing and probing strongly correlated quantum matter. A largely open question that may be addressed by such simulators is whether coupled critical states can combine into new non-Fermi liquid (NFL) phases. Inspired by the recent realization of a two-site charge-Kondo circuit [W. Pouse et al., Nat. Phys. 19, 492 (2023)], we uncover the fate of coupled Kondo anyons emerging from the two-channel-Kondo critical point at each site. Bosonization and quantum Brownian motion methods yield the full quasiballistic phase diagram and low-temperature transport properties, while numerical renormalization group calculations resolve the complementary weak-coupling limit. Together, these provide a unified description, and reveal robust NFL phases with continuously tunable transport and susceptibility exponents. Stronger inter-site coupling ultimately produces a screened Fermi liquid.