Abstract
The Tomonaga-Luttinger liquid (TLL) concept is believed to generically describe the strongly-correlated physics of one-dimensional systems at low temperatures. A hallmark signature in 1D conductors is the quantum phase transition between metallic and insulating states induced by a single impurity. However, this transition impedes experimental explorations of real-world TLLs. Furthermore, its theoretical treatment, explaining the universal energy rescaling of the conductance at low temperatures, has so far been achieved exactly only for specific interaction strengths. Quantum simulation can provide a powerful workaround. Here, a hybrid metal-semiconductor dissipative quantum circuit is shown to implement the analogue of a TLL of adjustable electronic interactions comprising a single, fully tunable scattering impurity. Measurements reveal the renormalization group `beta-function' for the conductance that completely determines the TLL universal crossover to an insulating state upon cooling. Moreover, the characteristic scaling energy locating at a given temperature the position within this conductance renormalization flow is established over nine decades versus circuit parameters, and the out-of-equilibrium regime is explored. With the quantum simulator quality demonstrated from the precise parameter-free validation of existing and novel TLL predictions, quantum simulation is achieved in a strong sense, by elucidating interaction regimes which resist theoretical solutions.
Highlights
In condensed-matter physics, a great challenge with abundant technological prospects is to understand the microscopic mechanisms of strongly correlated phenomena
II, we describe the experimental implementation of the Tomonaga-Luttinger liquid (TLL) model with an impurity for different values of the Luttinger interaction parameter K ∈ f1=2; 2=3; 3=4; 4=5g, we present signatures of the quantum phase transition between metallic and insulating states at the ballistic critical point, and we detail the model of our device
The device was operated at four different values of the Luttinger interaction parameter (K ∈ f1=2;2=3;3=4;4=5g), for which we completely determined the distinct conductance scaling flows to an insulating state as well as the relations connecting the scaling energy to the impurity scattering strength and explored the nontrivial crossovers from thermal to nonequilibrium regimes
Summary
In condensed-matter physics, a great challenge with abundant technological prospects is to understand the microscopic mechanisms of strongly correlated phenomena. The crossover of a 1D conductor comprising a single static impurity toward an insulating state is a trademark TLL signature exposing exotic features [27,30] It obeys a universal scaling flow, the determination of which counts among the most theoretically challenging Luttinger physics problems. Further technical details and additional measurements are provided in the Appendixes
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