Near-Schrödinger dynamics at large charge

Abstract

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.

Matches published version in PRD

References in corpus (5)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Selected Topics in the Large Quantum Number Expansion
• The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals
• Droplet-Edge Operators in Nonrelativistic Conformal Field Theories

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• How to Build a Black Hole out of Instantons
• Convexity, large charge and the large-N phase diagram of the ${\phi }^4$ theory