Journal of High Energy Physics

, 2018:52 | Cite as

The large-charge expansion for Schrödinger systems

  • Samuel Favrod
  • Domenico Orlando
  • Susanne ReffertEmail author
Open Access
Regular Article - Theoretical Physics


In this note, we perform the large-charge expansion for non-relativistic systems with a global U(1) symmetry in 3 + 1 and 2 + 1 space-time dimensions, motivated by applications to the unitary Fermi gas and anyons. These systems do not have full conformal invariance, but are invariant under the Schrödinger group. Also here, the low-energy physics is encoded by a Goldstone boson which is due to the breaking of the global symmetry when fixing the charge. We find that in 2 + 1 dimensions and higher, there is a large-charge expansion in which quantum corrections are suppressed with respect to the next-to-leading order terms in the Lagrangian. We give the next-to-leading-order expressions for the ground state energy and the speed of sound.


Effective Field Theories Global Symmetries Conformal Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Samuel Favrod
    • 1
  • Domenico Orlando
    • 2
    • 3
  • Susanne Reffert
    • 3
    Email author
  1. 1.Institut für Theoretische Physik, ETH ZürichZürichSwitzerland
  2. 2.INFN sezione di Torino, Arnold-Regge CenterTurinItaly
  3. 3.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland

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