One-dimensional (1D) systems at low temperatures form exotic phases of strongly-correlated matter believed to be generically described by the so-called Tomonaga-Luttinger liquid (TLL) concept. A hallmark signature in 1D conductors is that, when the temperature is reduced, even a single impurity can drive them into an insulating state. However, the extreme sensitivity of this metal-insulator transition impedes experimental explorations of real-world TLLs. Furthermore, its theoretical treatment has only been achieved exactly for specific strengths of interaction. I will show that a quantum simulator can provide a useful workaround : a hybrid metal-semiconductor dissipative quantum circuit (fig. 1a) implements a TLL analogue with adjustable electronic interactions and a fully tunable scattering impurity. Measurements reveal the renormalization group `beta-function' for the conductance (fig. 1b), which completely determines the scaling flow to an insulating state upon cooling. Moreover, we establish the quantitative scaling temperature versus model parameters and explore the out-of-equilibrium regime. The quantum-simulator quality is demonstrated from the precise parameter-free validation of existing and novel TLL predictions.

Coffee and pastries at 11h00.