Abstract
We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients. We show that there are fractonic modes with either subdimensional propagation or no propagation altogether, namely, immobility. Such a class of effective field theories encompasses instances of helical superfluids and metafluids, where fractons can be connected to an emergent symmetry under higher-moment charges, leading in turns to the trivialization of some elastic coefficients. The introduction of a finite-charge density alters the mobility properties of fractons and leads to a competition between the chemical potential and the superfluid velocity in determining the gap of the dilaton. The mobility of fractons can also be altered at zero density upon considering additional higher-derivative terms.
Highlights
An interesting aspect of low-energy effective theories is that of emergent symmetries
We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients
The Mexican hat model we have studied in the previous sections has a large emergent symmetry that results in the presence of trivial modes in the spectrum
Summary
An interesting aspect of low-energy effective theories is that of emergent symmetries. In the simplest setup of a complex scalar field with a Mexican hat potential, the Uð1Þ symmetry associated to phase rotations of the scalar is spontaneously broken and the low-energy effective theory is described by a massless Nambu-Goldstone boson. We want to explore low-energy effective theories with emergent symmetries that lead to (gapless) fractonic modes. An interesting case is when time translations are broken by a finite chemical potential Under these conditions some of the Nambu-Goldstone bosons become gapped when the effective unbroken Hamiltonian does not commute with some of the broken generators [34,35,36,37,38,39,40]. We have collected several technical results and generalizations to (3 þ 1) dimensions in the Appendixes
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