Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective

Proliferation of defects is a mechanism that allows for topological phase transitions. Such a phase transition is found in two dimensions for the XY model, which lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. The transition point can be found using renormalization group analysis. We apply renormalization group arguments to determine the nature of BKT transitions for the three-dimensional plaquette-dimer model, which is a model that exhibits fractonic mobility constraints. We show that an important part of this analysis demands a modified dimensional analysis that changes the interpretation of scaling dimensions upon coarse-graining. Using this modified dimensional analysis, we compute the beta functions of the model and predict a finite critical value above which the fractonic phase melts, proliferating dipoles. Importantly, the transition point is found through a renormalization group analysis that accounts for the phenomenon of UV/IR mixing, characteristic of fractonic models.

Figure 1

Constant-energy surfaces.

Figure 2

The deformation of the momentum shell to one that is parallel to the $k$ direction.

Figure 3

The deformation of the momentum shell corresponding to Eq. (28) but where the limits of the $\widehat{q}$ integral are not divided by $\widehat{p}$.

Figure 4

RG flow diagram for the rescaled coefficient ${\tilde{\kappa }}_{xy}$ and fugacity ${\tilde{\alpha }}_d$.