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

The European Physical Journal Special Topics volume 229, pages 663–682 (2020)Cite this article

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.

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Authors and Affiliations

  1. Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Univ Paris Sud, Université Paris-Saclay, 91120, Palaiseau, France

    Anne Anthore & Frédéric Pierre

  2. Université de Paris, Univ Paris Diderot, 75013, Paris, France

    Anne Anthore

  3. Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology, 52056, Aachen, Germany

    Dante M. Kennes & Volker Meden

  4. Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques (MPQ), Univ Paris Diderot, CNRS, 75013, Paris, France

    Edouard Boulat

  5. Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, 72076, Tübingen, Germany

    Sabine Andergassen

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  1. Anne Anthore
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  2. Dante M. Kennes
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  3. Edouard Boulat
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  4. Sabine Andergassen
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  6. Volker Meden
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Correspondence to Volker Meden.

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Anthore, A., Kennes, D.M., Boulat, E. et al. Universality at work – the local sine-Gordon model, lattice fermions, and quantum circuits. Eur. Phys. J. Spec. Top. 229, 663–682 (2020). https://doi.org/10.1140/epjst/e2019-900117-5

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  • DOI: https://doi.org/10.1140/epjst/e2019-900117-5