Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory

Author:

Beane Silas R.12ORCID,Orlando Domenico314,Reffert Susanne31ORCID

Affiliation:

1. Universität Bern

2. University of Washington

3. Kyoto University

4. INFN sezione di Torino

Abstract

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in nonrelativistic conformal field theory is obtained. This field is used to compute Schrödinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge. Published by the American Physical Society 2024

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

U.S. Department of Energy

Publisher

American Physical Society (APS)

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