Odd Fracton Theories, Proximate Orders, and Parton Constructions

• URL: http://arxiv.org/abs/2004.14393v1
• Date: Wed, 29 Apr 2020 18:00:02 GMT
• Title: Odd Fracton Theories, Proximate Orders, and Parton Constructions
• Authors: Michael Pretko, S. A. Parameswaran, Michael Hermele
• Abstract summary: We describe a framework to characterize the action of symmetry on sub-dimensional fractional excitations. We show that X-cube fracton order can occur only at integer or half-odd-integer filling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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