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arXiv · 2403.18898

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

Silas R. Beane·Domenico Orlando·Susanne Reffert
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Abstract

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr\"odinger-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 Schr\"odinger 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.

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Silas R. Beane, Domenico Orlando, Susanne Reffert. 2024-03-27. Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory. https://doi.org/10.1103/physrevd.110.025011

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