Near-Schrödinger dynamics at large charge

In this paper we discuss a nonrelativistic system at large charge in a regime where Schrödinger symmetry is slightly broken by an explicit mass term for the dilaton field which nonlinearly realizes nonrelativistic 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 nonrelativistic state-operator correspondence. As a signature of the explicit breaking, we identify a √{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.