Abstract
We study operators in Schrödinger 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 spatial dimensions. These results apply to theories with a superfluid phase, such as unitary fermions or critical anyon systems.
Highlights
133Cs [21], 85Rb [22],39K [23], and various spin chain models [24]
We study operators in Schrodinger invariant field theories with large charge and spin
We find a diverse set of scaling behaviors for non-relativistic conformal field theories (NRCFTs) in both d = 2 and d = 3 spatial dimensions
Summary
We briefly review the superfluid hydrodynamics in the Hamiltonian formalism, specialized to the case of a Schrodinger invariant system in a harmonic potential. We’ll be interested in excited state configurations which carry some angular momentum These will correspond to spinful operators in the large charge sector of the NRCFTs which the superfluid EFT describes. The other configuration of a superfluid that can support angular momentum is a vortex, which gives rise to a singular velocity field of the condensate This is a distinct semi-classical saddle point which is not related to the ground state. These two excitations, phonons and vortices, are the configurations of the superfluid we know support angular momentum. By answering this and using the superfluid EFT defined above we compute the scaling behavior of operators carrying charge and angular momentum
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
