Odd fracton theories, proximate orders, and parton constructions

Journal article

The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy nontrivial 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 subdimensional 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 conventionally 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.

Authors: Pretko, M; Parameswaran, SA; Hermele, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review B
• Volume: 102
• Issue: 20
• Pages: 205106
• Publication date: 2020-11-06
• Acceptance date: 2020-10-23
• DOI: 10.1103/PhysRevB.102.205106
• EISSN: 2469-9969
• ISSN: 2469-9950
• Language: English
• Keywords: FFR