Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

Abstract

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For $d$-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}4$, while dipole symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$. For $T=0$, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$ if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.