Near-Schrödinger dynamics at large charge


In this note we discuss a non-relativistic system at large charge in a regime where Schrödinger symmetry is slightly broken by an explicit mass term for the dilaton field which non-linearly realizes non-relativistic scale invariance. To get there, we first develop the large-charge formalism from the linear sigma model perspective, including the harmonic trapping potential necessary for the non-relativistic state-operator correspondence. As a signature of the explicit breaking, we identify a $\sqrt{Q} \log(Q)$ term which, depending on the space dimension, is either of the same order as the effects coming from the breakdown of the EFT at the edge of the particle cloud, or can be distinguished from these effects over a large range of orders of magnitude.