Odd Fracton Theories, Proximate Orders, and Parton Constructions

Abstract

The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy non-trivial conditions on their low-energy properties when a combination of lattice translation and $U(1)$ symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other sub-dimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that "odd" versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd $Z_2$ gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry-breaking, thereby allowing us to identify a class of conventional ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. Condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.

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Cited by in corpus (7)

• Fractonic superfluids. (II). Condensing subdimensional particles
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• (Four) Dual Plaquette 3D Ising Models
• Planon-modular fracton orders