# The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals

## TL;DR

This paper explores the properties of operators with large charge and spin in non-relativistic conformal field theories, linking them to superfluid states with phonons and vortices, and computes their scaling behaviors.

## Contribution

It introduces a novel analysis of large charge and spin operators in NRCFTs using effective field theory, revealing diverse scaling behaviors in different dimensions.

## Key findings

- Operators correspond to superfluid states with phonons or vortices
- Computed operator dimensions using effective field theory
- Identified diverse scaling behaviors in 2D and 3D

## Abstract

We study operators in Schr\"odinger invariant field theories (non-relativistic conformal field theories or NRCFTs) with large charge (particle number) and spin. Via the state-operator correspondence for NRCFTs, such operators correspond to states of a superfluid in a harmonic trap with phonons or vortices. Using the effective field theory of the Goldstone mode, we compute the dimensions of operators to leading order in the angular momentum $L$ and charge $Q$. We find a diverse set of scaling behaviors for NRCFTs in both $d=2$ and $d=3$.