Circuit Quantum Simulation of a Tomonaga-Luttinger Liquid with an Impurity

TL;DR

This paper demonstrates a quantum simulation of a Tomonaga-Luttinger liquid with an impurity using a hybrid metal-semiconductor circuit, revealing universal conductance behavior and exploring regimes difficult for traditional theory.

Contribution

It introduces a tunable quantum circuit that simulates a TLL with an impurity, enabling experimental access to complex interaction regimes and universal conductance scaling.

Findings

Measured the conductance renormalization group `beta-function'

Established the scaling energy over nine decades

Validated TLL predictions with parameter-free precision

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.