Eur. Phys. J. Special Topics 229, 663–682 (2020)
https://doi.org/10.1140/epjst/e2019-900117-5

Review

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

¹ Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Univ Paris Sud, Université Paris-Saclay, 91120 Palaiseau, France
² Université de Paris, Univ Paris Diderot, 75013 Paris, France
³ Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
⁴ Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques (MPQ), Univ Paris Diderot, CNRS, 75013 Paris, France
⁵ Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, 72076 Tübingen, Germany

^a e-mail: meden@physik.rwth-aachen.de

Received: 18 June 2019
Received in final form: 12 August 2019
Published online: 14 February 2020

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.