Fractonic plaquette-dimer liquid beyond renormalization

Abstract

We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation 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 analyse 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.

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• Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
• Classical Non-Relativistic Fractons
• Non-invertible duality and symmetry topological order of one-dimensional lattice models with spatially modulated symmetry
• Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective
• A post-Gaussian approach to dipole symmetries and interacting fractons
• Machian fractons, Hamiltonian attractors and non-equilibrium steady states
• Fractonic criticality in Rydberg atom arrays
• Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas
• Hollow Lattice Tensor Gauge Theories with Bosonic Matter
• Continuum Fractons: Quantization and the Few Body Problem