Quantum critical states and phase transitions in the presence of non-equilibrium noise

Journal name:
Nature Physics
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Published online


Quantum critical points are characterized by scale-invariant correlations and therefore by long-range entanglement. As such, they present fascinating examples of quantum states of matter and their study is an important theme in modern physics. However, little is known about the fate of quantum criticality under non-equilibrium conditions. Here we investigate the effect of external noise sources on quantum critical points. It is natural to expect that noise will have a similar effect to finite temperature, that is, destroying the subtle correlations underlying the quantum critical behaviour. Surprisingly, we find that the ubiquitous 1/f noise does preserve the critical correlations. The emergent states show an intriguing interplay of intrinsic quantum critical and external-noise-driven fluctuations. We illustrate this general phenomenon with specific examples describing solid-state and ultracold-atoms systems. Moreover, our approach shows that genuine quantum phase transitions can exist even under non-equilibrium conditions.

At a glance


  1. Effects of non-equilibrium noise on the localization quantum phase transition of a single shunted Josephson junction:
    Figure 1: Effects of non-equilibrium noise on the localization quantum phase transition of a single shunted Josephson junction:

    a, Electronic circuit relevant to a resistively shunted Josephson junction with charging noise. b, Critical resistance R/RQ as a function of the noise strength F0, in the weak coupling limit. c, Critical conductance R/RQ as a function of the noise strength F0, in the strong-coupling limit. b and c are related by the duality transformation R/RQ RQ/R and ‘superconductor’ ‘normal’. d, Schematic phase diagram at equilibrium (dotted line) and in the presence of non-equilibrium 1/f noise (dashed line).

  2. Effects of non-equilibrium noise on the response to Bragg spectroscopy.
    Figure 2: Effects of non-equilibrium noise on the response to Bragg spectroscopy.

    a, Imaginary part of the response function χ′′(q,ω) in a one-dimensional system with K=0.5, at equilibrium (F0=0). b, The same plot as in a, in the presence of a strong 1/f noise with F0/η=4π2.


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  1. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

    • Emanuele G. Dalla Torre &
    • Ehud Altman
  2. Department of Physics, Harvard University, Cambridge Massachusetts 02138, USA

    • Eugene Demler
  3. DPMC-MaNEP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva, Switzerland

    • Thierry Giamarchi


All authors contributed equally to this work.

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