Fractonic plaquette-dimer liquid beyond renormalization

TL;DR

This paper explores a generalized tiling model combining dimers and plaquettes on an anisotropic lattice, revealing a fracton-like electrostatics framework with a novel phase transition akin to a fracton Kosterlitz-Thouless transition, characterized by UV-IR mixing.

Contribution

It introduces a new class of fractonic tiling models with a detailed analysis of their phase transition and UV-IR mixing effects, extending fracton physics beyond traditional renormalization approaches.

Findings

Identification of a fracton electrostatics in tiling models

Demonstration of a phase transition driven by defect dipole proliferation

Discovery of UV-IR mixing dominating low-energy behavior

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.