Universality at work -- the local sine-Gordon model, lattice fermions, and quantum circuits

TL;DR

This paper demonstrates that diverse physical systems, including field theories, lattice fermions, and quantum circuits, exhibit universal low-energy behavior near a quantum critical point, highlighting emergent universality across different physics domains.

Contribution

It shows that universal low-energy scaling curves of conductance are consistent across models and experiments despite different high-energy physics, establishing a bridge between theory and experiment.

Findings

Universal low-energy conductance scaling curves match across models and experiments.

Emergent quantum phase transition between metallic and insulating states.

Universal physics arises from a common quantum critical point.

Abstract

We review the intriguing many-body physics resulting out of the interplay of a single, local impurity and the two-particle interaction in a one-dimensional Fermi system. Even if the underlying homogeneous correlated system is taken to be metallic, this interplay leads to an emergent quantum phase transition between metallic and insulating states. We show that the zero temperature critical point and the universal low-energy physics associated to it, is realized in two different models, the field theoretical local sine-Gordon model and spinless fermions on a lattice with nearest-neighbor hopping and two-particle interaction, as well as in an experimental setup consisting of a highly tunable quantum circuit. Despite the different high-energy physics of the three systems the universal low-energy scaling curves of the conductance as a function of temperature agree up to a very high precision without any free parameter. Overall this provides a convincing example of how emergent universality in complex systems originating from a common underlying quantum critical point establishes a bridge between different fields of physics. In our case between field theory, quantum many-body theory of correlated Fermi systems, and experimental circuit quantum electrodynamics.