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Strongly correlated electrons
Abstract:
We consider close-packed tiling models of geometric objects-a mixture of hardcore dimers and plaquettes- as a generalization of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a z link or a plaquette in the x -y plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type "higher-rank electrostatics," which can exhibit a plaquette-dimer liquid and an ordered phase. We analyze this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low-energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.
